Si tu utilises un article indéfini : « un ami » c’est tout de suite évident que tu ne parles pas de ce type de relation (ou alors il faudrait que tu prononces un d’une manière ambiguë et marquée).
Sinon tu as un synonyme à un niveau de langage moins soutenu « pote » qui devrait faire l’affaire.

We’d say :

• ma petite amie for girlfriend
• mon petit ami for boyfriend

So ami/e needs to be qualified as petit/e to convey an amorous relationship. You can tell your teacher that for sure.

I think that petit(e) ami(e) is somewhat old fashioned (an over fortyish thing perhaps?). Younger generations will talk of mon copain or ma copine. With the possessive pronoun in front of the noun amorous relationship is involved and it does not sound ambiguous at all.

On the other hand I have heard older people (a pre WW2 thing perhaps ?) talk of mon bon ami et ma bonne amie (use of bon/bonne ) but that could be ambiguous because it was also a form of address to someone who was not particularly your friend or that you did not particularly know. It could be used to convey a patronizing attitude towards an inferior.

« Mon ami(e) » peut exprimer une relation d’amitié ou d’amour suivant le contexte, voire entretenir l’ambiguïté. Mais par défaut, tu peux considérer que la relation est de l’amitié. Ce n’est qu’avec certains adjectifs qu’ami exprime explicitement une relation amoureuse : « mon petit ami / ma petite amie » (courant, surtout chez les adolescents), « mon bon ami / ma bonne amie » (rare en français actuel). « Mon ami(e) » peut signifier une relation amoureuse, mais en général seulement si le contexte le laisse par ailleurs apparaître. Le Trésor de la langue française traite de ces cas dans la section I.A.2 (j’omets ici les exemples) :

2. [L’attachement inclut la relation amoureuse]
a) [L’accent est mis principalement sur la nature sentimentale de l’attachement]
    (exemples où le contexte rend apparent que ce n’est pas le sens habituel)
b) Par euphémisme ou pudeur. [L’accent est mis principalement sur la nature physique de l’attachement, avec une idées de relations avant ou hors ou sans mariage]
— Langue commune (surtout au féminin, avec une épithète de valeur affective). Bon(ne), petit(e) ami(e).
— Synonyme noble ou mondain de amant, maîtresse

Dans l’usage courant, « mon ami(e) » s’emploie quelquefois pour désigner quelqu’un avec qui l’on a une relation amoureuse stable hors mariage, mais ce n’est pas l’interprétation la plus courante, elle nécessite souvent de préciser qu’il s’agit d’un « common law spouse » et pas d’un simple friend. La facilité de passer à l’interprétation amoureuse dépend peut-être des régions ou des classes sociales.

Toutefois, en général, on dira plutôt « un(e) ami(e) » la première fois que l’on parle de la personne, et « mon ami(e) » les fois suivantes, parce que l’adjectif possessif a un caractère défini : c’est l’ami de moi dont j’ai parlé précédemment (mon ami = my friend, un ami = a friend (of mine)).

Pour le mot copain, c’est l’inverse : « mon copain / ma copine », c’est une personne avec laquelle on entretient une relation amoureuse, sauf si le contexte indique le contraire. C’est ce mot qu’on peut plus rapprocher de boyfriend / girlfriend, bien que l’utilisation non amoureuse reste plus courante en français qu’en anglais.

I have a friend that lives near my house. My friend likes waffles. → J’ai un ami qui habite près de chez moi. Mon ami aime les gaufres.
I’m going to travel with my friend. → Je vais partir en voyage avec un ami.
I’m going to travel with my girlfriend. → Je vais partir en voyage avec ma copine.
My friend Charlie will come with me. → Mon ami Charlie va m’accompagner.

It is just not true to consider “mon ami” or “mon amie” means an amorous relationship. People may use “ami” to refer to such a relation, but as already told unless the context is different, it refers to a friendship.

The choice of the pronoun can change the meaning too. For example, suppose you are invited to a party:

• “Je viendrai avec mon amie.” is not very clear. It is likely to refer to a girlfriend but may equally refer to a friendship.
• “Je viendrai avec une amie.” is clearly referring to a friendship.
• “Je vous présente mon amie, Laure.” is likely referring to a friendship. The behavior might make the meaning different though.

If you are looking to other ways of referring to friends, you can use:

• “une connaissance”, which refers to a weak relation, an “acquaintance”
• “un/une pote”, which is familiar and basically means “buddy”
• “un ami/une amie”
• “un (très) bon ami/une (très) bonne amie”, which means “a (very) good friend” and leaves no doubt it is a friendship
• “un ami (très) proche/une amie (très) proche”, “a (very) close friend”
• “mon meilleur ami/ma meilleure amie”, to refer to your best friend

On a personal note, I always had the feeling that “ami” in French has a very strong meaning, stronger than “friend”. But maybe it is just my interpretation of the word.

On a side note, children will often use “copain/copine”. This is much less usual for grown ups, especially since those are way more likely to refer to a date as soon as you enter teen age.

The familiar “pote” is another way to avoid any ambiguity, as it doesn’t have the “boyfriend” signification at all.

I have a friend that lives near my house.
J’ai un pote qui habite près de chez moi.

I’m going to travel with my friend.
Je vais voyager avec mon pote.

But the downside of it is that it’s indeed quite familiar. You could also use “camarade” in some contexts; maybe not as a translation of “friend” but rather of “mate” though.

My roommate didn’t come home up until 1am.
Mon camarade de chambre n’est pas rentré avant 2 heures du matin.¹

Didn’t your classmates tell you there was a test today?
Vos camarades de classe ne vous ont-ils pas dit qu’il y avait une interro aujourd’hui ?

As for the usage of “ami” by itself, mostly the context should make it clear whether it’s more than just a friend, unless it’s left unclear on purpose; but other answers covered that better than I could.

^{1. Taking into account the time zone difference between France and the UK, of course.}

“mon ami(e)” is an old way to say my girl/boyfriend. Even if it is almost not used anymore. People avoid it because it may still be ambiguous, I almost never heard that.

People can say “un ami”, “un pote”, “un de mes amis”.

For instance, “Je vais diner avec un ami/pote.” is very clearly about friendship, and it’s also clearly about “my friend”.

The sentence “My English friend comes to Paris.” would be translated by “J’ai un ami anglais qui vient à Paris.” or “Un de mes potes anglais vient à Paris.”

As a Canadian, Quebecers call their girlfriend and boyfriend: un chum (mas)or une chum (fem).

“I have a friend that lives near my house” = «J’ai un ami qui habite loin de ma maison»

I have no idea what people call their girlfriend or boyfriend in France but I hear its une copaine for girlfriend and un copine for boyfriend

“mon fiancé, ma fiancé” is now used to refer to a close relationship, almost a couple in France now, the word and full meaning of the word fiancé was changed by law some years ago. Now used in France to show a very close relationship with no firm intention of marriage. Often a man will call his lover or beloved “wife” meaning a deeply close love. My French lover calls me my wife, a strong way to say deeply beloved. The name fiancé is now the word used to say “my girlfriend” in France. In England this word means an intention to Marry, not so in France.

 

In French, ami(e) and copain/copine can correspond to friend in English, depending on the context.

Etymologically, un(e) ami(e) is someone you love/like (amo, as, are in Latin -> Aimer/ to love) whereas un copain/une copine is someone you share pain [=bread] with.

In France, the relationship you have with a person can determine whether it’s your copain or ami. You’d for example have a ami you’ve known for quite a long time, and have a copain that you know from work and with whom you don’t share an intense friendship. There also is a tendency to add the adjective petit [=small] to either ami or copain in order to mean boyfriend/girlfriend.

However, copain/copine can sometimes be understood, in French and according to context (people you’re talking to, discussion etc.), as your significant other.

For instance, if a lady/girl/woman says :

Mon copain travaille à la banque.

Or a guy/boy/man says :

Ma copine travaille à la banque.

And that the context has references to couples and love relationships, then it takes the meaning of boyfriend/girlfriend. Otherwise, if the people in the discussion are talking about friends, then it’s understood as friend in general.

If the context isn’t really constant/set, use ami as it doesn’t have that kind of nuance.