Your symptoms may certainly be due to a prostate infection. Unfortunately, they can be notoriously difficult to treat.
To answer your question, it is definitely possible to have a urinary tract infection without any overt discharge.
One of the more useful tests would be a prostatic massage which could exude prostate secretions which can be cultured. Appropriate antibiotic treatment can last from 4-12 months.
I would also recommend a prostate ultrasound to look for a prostatic abscess if antibiotics are not helpful.
Regarding the black stools - they may be secondary to an upper GI bleed - I would have this looked at by your physician for a possible endoscopy.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Thanks,
Kevin, M.D.