Hmm, sometimes doctors and patients alike are buffled when antibiotics don't work.
The reason could be antibiotic resistance, which is more
prevalent nowadays or inadequate/flawed testing
to verify the infectious pathogens are not bacteria.
You need to rule out the possibility of a yeast/fungal infection which may be present in the urethra, or Balanitis,
both of which would get worse with the intake of antibiotics!
Prostatitis, as the other poster mentioned, specially non-bacterial prostatitis, should also be ruled out.
Ask your GP, if s/he can help you with this.
Best wishes,
Niko
Get your prostate checked, could be prostatitis