Sick makes me think of the character in Amityville Horror or maybe Jason...it's not a nice word to use. My mother also had MS most of my life until she passed in 2008, so I will usually think of physical illness when I hear "sick", although she was also mentally ill as it had shrunk her brain and she could barely speak anymore and had other mental complications (she had the progressive kind).
Sick just has a bad connotation to it all around; I would definitely speak to your T re: a replacement word. You don't sound "sick" at all...you are able to express yourself and seem quite self-aware. The word seems totally inappropriate and it would bother me, too.
I had my T call one of my relationships "contaminated" (and I really care about this person...and it's not like he ever physically or mentally abused me, either...he is super nice). I don't think my T could think of a replacement word, either. So I'm stuck with that...my relationship with this person was fine until X happened and then it was "contaminated". REALLY not ok with that. I have to find another word myself... I was using "got complicated" before and that seems to be pretty fitting.
Ts can be so thoughtless. And btw, ever notice how most Ts are so careful to call us "clients" and not "patients"? At least, mine have been.
Hugs to you, and hopefully you can get/find a more fitting, supportive word!