Hello Dude, welcome to the site.
A lot of people hop onto the net and read up all about the antidepressants (AD), especially the side-effects, but these need to be mentioned, both good and perhaps bad reactions, because if they don't then they could be taken to court, so they do this to protect themselves, however, you might not react the way it says and you will only know once you begin taking them.
You would usually be put on a low dose to begin with just to see how they go and then possibly slowly increased over time.
Are you seeing a psychiatrist as well as a therapist and if so, then the latter maybe against medication, but if CBT isn't working to its full extent then perhaps starting on AD might be the answer, and I'm not a qualified doctor to say this, only know from experience.
I can't tell you what to do, but maybe suggest you give them a try, and remember if they don't agree with you or make you feel any better with 6 weeks, then there are many other types of AD's, but you can stop under the guidance from your doctor.
Let us know how you get on.