The nasty comments made by strangers on the social media platforms about the actor made him ______________

The phrase " to be ill at ease" means to be uncomfortable or embarrassed. This fits well in the context of someone reacting to nasty comments on social media. 

"Ill at heart" or ill in heart" are not standard English idioms.

"Ill and ache" is grammatically incorrect. This is because ill is an adjective, whereas ache is a verb. Using them together mixes the parts of speech without a clear or correct grammatical connection. 

So, option A is the best choice.