Your symptoms do sound like prostatitis (and not prostate cancer, which isn't painful in the prostate).
It is usually a bacterial infection, but as Lyn said, it often doesn't come out in urine. It also often doesn't come out in semen (which some doctors will ask for a sample to culture) because the prostate ducts where it is have got blocked off.
You might ask for Tamsulosin temporarily to improve your flow rate, and reduce chances of going in to retention (not being able to pee). The slow flow rate is what causes going regularly, because you aren't emptying your bladder, so it fills up sooner again. (You can buy Tamsulosin off-prescription from a pharmacy for a short period, but I strongly suggest you ask your GP so they can be sure it's suitable for you, and aware you are taking it.)
You need to ask for a referral to urology, if antibiotics alone don't fix it. (They often don't, because they also can't get to the parts of the prostate with infection.) Sometimes they cause short term relief because they are also anti-inflammatory, but if the symptoms come back very soon afterwards, then they didn't actually work.
One other warning, if one of the antibiotics is Ciprofloxacin (which is very likely), avoid putting heavy forces on your tendons during and for a while after finishing the antibiotic, as it can cause tendon weakness.