“Je suis encore malade” means “I’m still sick”. “J’en suis encore malade” means “I’m still sick due to this” or more likely “I’m still feeling uneasy about this” or “I’m still angry about this”. The adverb en stands for the reason for the illness or anger. It is always placed before the verb, you can’t say “*je suis encore en malade”.

Usually, malade means sick, ill. However, in some contexts, it can refer not to a sickness but to a general feeling of uneasiness, discontent or even anger. “J’en suis encore malade” evokes that alternate meaning by default.

On m’a piqué mon vélo la semaine dernière. J’en suis encore malade.
Someone stole my bike last week. I’m still mad about it.

En is a pronoun which replaces a complement introduced by de. For instance,

J’achète des fruits. <-> J’en achète.

It can be a complement of a verb (like in the previous example) or in some cases a noun (I think the noun itself must be direct object of the verb or an attribute linked to the subject by a copula verb).

Il a peur des chiens. <-> Il en a peur.

Je suis malade d’avoir mangé des fruits pas frais. <-> J’en suis malade.