Does this sound like depression? Can depression make you physically exhausted? To the point of feeling sick?
This does sound like depression to me. For me, it was a feeling really similar to exhaustion. It's like the depression makes you not want to do anything, and you start to lose interest in activities that used to energize you. In my case, the feeling sick part came from the physical part of depression, which involved an almost constant "kicked in the gut" type of feeling.
I have never taken Wellbutrin, but I did take Prozac for almost a year and a half, which falls into the same family of medicines as Wellbutrin. The antidepressants really did help me get on my feet, and along with a lot of hard work in IC and reading, I was eventually able to wean myself off of the antidepressants.
I guess the only advice I can give you is to make sure you are dealing with an MD that has experience with mental health (someone like PurpleJacket, who is a member of this site, for example), or even make an appointment with a psychiatrist. There are multiple medicines within the category of SSRI's, and they each have their own side affects, and they work slightly different, and impact people in different ways.
I have absolutely no medical training, so definitely listen to your physician first, with due diligence of course.
Best of luck to you!