Unfortunately, prostatitis will often not respond to many antibiotics.If antibiotics don't get it, they usually just treat any symptoms. It can relapse and remit periodically. Other causes of elevated PSA are BPH/enlarged prostate (unlikely at your age), prostate cancer (unlikely at your age), acute urinary retention (any problems peeing?), and temporary blips from sex, bike riding, etc.
There is a new test called PHI that is much better than PSA at separating the increase in PSA from prostate cancer from the PSA caused by all those other things. Your doctor may not be aware of it because it just became available in the US (it's been used in Europe for many years).
Here's a link to the site from which you can order the test. Unlike some other tests, insurance covers it or it's free. You can email the link to your urologist and ask him to order it for you.
- Allen