Greetings.
Gonorrhea in men is usually very symptomatic: in older non-English books there was a term "eye-popping pain" to describe it. It is theoretically possible to have gonorrhea with little pain and little discharge, but it is not likely.
And yes, it can't start in bladder.
No other STIs produce symptoms you describe.
If you are over 40, acute prostatitis is much more likely to fit your symptoms. It may also be a mild urethritis caused by normal (non-STI) bacteria.
Unless there are obvious urethral symptoms (sharp pain during urination, strong burning sensation at penis tip) or any other obvious symptoms I would not worry too much.
If you can't take your mind off it, it is always a good idea to get tested.