What are your symptoms? Most likely the diarrhea is from the antibiotics. You should probably look into taking some probiotics to restore the flora that has been decimated by the antibiotics. Remember the antibiotics kill most bacteria, good and bad and without the good you can get intestinal issues, thus the diarrhea. Yes, prostatitis can be caused by sexually transmitted bacteria that is not necessarily chlamydia or gonorrhea (perhaps E. Coli or NGU or many others). To be honest, hopefully your prostatitis was caused by a bacterial infection (acute prostatitis) since that is the easiest to treat (you're doing it now with the floroquinolone antibiotic aka Levaquin). If it isn't acute and continues on to be chronic (lasting more than 3 months) then that's where things get difficult (as I can attest). Good luck!
It is possible that a STD could cause it, but also other things can cause it. You have been treated for STD's so I would probably rule out a STD as the cause.