I don't think that this is something you should worry about, especially since the person you are worried about is merely a character. Although I don't know any empaths, I do know plenty of counselors and as long as they don't get too emotionally invested in their client's problems, they're fine. People who become counselors went to school and trained to know how to deal with other people's emotional problems without getting too invested. Also technically all people suffer so suffering isn't something that's new.
By the way, an empathic counselor reminds me of Deanna Troi from Star Trek: The Next Generation. I'm not sure if she's the character you are referring to, but she is part Betazoid which makes her empathic and she works as the counselor on the galaxy class starship Enterprise-D.