Burning in the urine is due to inflammation of the urinary tract - bladder
, prostate, or the urethra
.Bladder and urethral infection will be easily detected on urine tests as bacteria are readily shed from these structures.
But prostate being a deep seated gland can escape the normal urine tests and hence return a negative result despite being inflamed or infected.
So a repeat urine test is recommended after a mild prostate massage which may squeeze out some pus cells or bacteria into the urine.If it is indeed due to infection, a course of antibiotics is recommended to get rid of it.As it is a deep seated gland , drugs also reach the gland with difficulty.Hence antibiotics have to be taken for longer periods (4 weeks).
Prostate inflammation could be sometimes without an infection.It could be stress induced.There is no particular reason why this happens, but it is commonly in periods of stress like anxiety, heavy work, traveling, hot climates etc.
In that case a course of anti-inflammatory drugs with prostate muscle relaxant like alfuzosin will help with the condition.
Another possibility is a hard plaque in the penis also known as peyronie's disease.Since you mentioned a hard structure,this possibility comes out.But there is associated pain and bending of penis during erections in this condition which you don't have.So chances that you have a peyronie's disease is less.
I would suggest you to get a repeat urine test after a short prostate massage.If there is evidence of infection, treat it with antibiotics.If not try the anti-inflammatory and alfa blockers foe some days.
If the problem still persists then a cystoscopy is mandatory.It involves seeing inside of the urethra and the bladder.Sometimes small growths can produce burning sensation.
Again no blood seen in the urine makes it less likely.
I hope this gives you some info to go forward with your problem and tackle it more efficiently and quickly.
If you have any doubts ,please let me know.