I'm a little unclear about whether you were tested for mono or just guessing about it. When I had mono some 30+ years ago the physical symptoms (fever etc) didn't last more than a few weeks but the exhaustion and depressed feeling lasted for a long time, 6-12 months as I recall though it could have been longer. It didn't just magically go away, it was gradual until one day I didn't worry about it anymore.
My daughter is struggling to overcome depression and anxiety that were triggered by an illness (not mono, but either a virus or lymes disease) 18 months ago so it can go on a long time. She is doing better but not back to normal yet and she did try an AD that she's now discontinuing.
You really should see a doctor to try to sort this out.
Firstly, you need the follow up appointment with your doctor. If you are on the wrong medication, you will need the doctor to help you find the right one.
I am not a doctor....but these are my thoughts through my own experiences.
Depression medication, gives you breathing space to sort out the problems. I dont think it is a magical "fix-all" cure, but it may help you get the room you need to sort yourself out.
Finally, I am not a fan of Zoloft, it did not agree with my brain. Understand that it is a mixture of the famous Stillnox and Prozac. I was taking Zoloft for a few months...then one day I had organised to go out to dinner with my family, I was all excited....and I thought "bugger it, I want to die now"....so I overdosed.....then once they let me out of the crazy hospital.....I did it again. Thus ends my relationship with Zoloft. That is just me though..everyone is different. But my point is....you need to stay in touch with your doctor.