I definitely think your problem is most likely the SSRI medication. It is possible that you could be asexual, but I think it's more likely the meds lowering your sex drive. Have you considered going off of it and see how you feel?
I have anxiety and panic attacks and I just started taking an SSRI for it as well, I've only been on it for 2 weeks, but I haven't really noticed any side effects or any real change yet.