I agree with BonzoDog. It sounds like your second doctor was better but not great in terms of tackling a long term, chronic problem. Why do you have a chronically inflamed prostate gland? That's the question. But regardless, you need a long term plan to deal with it. The cause can remain unknown. As bonzodog says, it is not always bacterial. It may not be able to be cured which stinks. But you then have to move into the area of controlling symptoms. Here's causes of chronic prostatitis:
a blockage of the flow of urine
microorganisms from sexually transmitted diseases like chlamydia
an immune system attack on the prostate
uric acid, a compound in urine, causing irritation in the prostate
abnormal functioning of nerves or muscles
These are the things you should get checked by your next urologist. Or this one who you are not yet FULLY sure will not want to help you adequately further.
To rule out bacterial reasons, antibiotics are usually tried for a full 12 weeks. Was this as long as your treatment? After that, it gets into relieving symptoms using things like muscle relaxers, yes, some pain killers but be very very careful there (addiction is not something you want to have enter your life) and anti anxiety medication. What do Nsaids do for you since they have the property that decreases inflammation? In theory, they should help! Also life style things like diet, proper rest and nutrition. And . .. prostate massage.
Here's a link: https://www.medicalnewstoday.com/articles/322457.php
Let us know what happens.
I would DEFINITELY seek out a different Uro - hopefully he/she will find smthg the other missed. Yes, it would be normally very young for you to have a prostrate prblm such as BPH (prostate enlargement) or cancer, but these DO occasionally occur in younger men. But more likely, you are dealing with chronic prostatitis - this is a very tricky disease, there is a bacterial type but also a non- bacterial type & either one can be very hard to eliminate. I had chronic prostatitis for a cpl yrs in my mid-late 30s & at times it seemed like it would never go away, but it did, finally. See if you can talk to your reg Dr & get a referral to a Uro who has some patience in getting to the bottom of it. You may need to try several different antibiotics as well as some other treatments, but don’t give up - in most cases, it does eventually resolve.
Best of luck & let us know if you get resolution...