Until you get some tests and results we can't know anything. At the moment the statistics are on your side.
The following stats are based on size of population, number of men diagnosed each year, number of deaths each year, and accuracy of PSA tests. I can't quote sources for these figures, though you can find them on the internet. I have made interpolations and estimates to try and present the figures in a meaningful way.
If you took 100 random 50 year olds and PSA tested them about 40 would come back with an elevated PSA. If you biopsied those 40 about 25 would have signs of cancer, and if you biopsied the other 60 who 'passed' the test about 10 would have signs of cancer.
Of those 35 who were diagnosed by the biopsy only 1 would have disease which needed immediate treatment. Of the 34 remaining 24 will die from other courses before the cancer develops sufficient to kill them, and 10 would go on to need treatment before the age of 70. Knowing which 10 of the 34 that would become serious is unknown. So you would put 24 men on to the treatment pathway who need not be there yet.
Of course you have LUTS and it is probably not a UTI (no test is 100% accurate so you may still have a UTI). BPH or enlarged prostate are other causes of LUTS.
If for my original 100 men you only took men with LUTS you would probably raise the diagnosis rate by 50%.
If you were looking for a 50 year old with stage 4 cancer you would need to increase the sample size to about 100,000 to find someone with stage 4 prostate cancer (we have had 10s if not 100s of people on this site who were diagnosed in their 40s or early 50s T2 or T3 but who were in hindsight already T4. But the sample size is about 15 million males over 40 over a 20 year period).
Back ache is so common in an animal that evolved to hang from branches (stretching back) to standing on two legs (compressing back) that it doesn't change the statistics at all, it is pretty much the price of being human.
So as I said at the start of this post the statistics are definitely on your side. But only tests will let us know for certain.