I am sure Dr Lee can answer the question, but since the prostate surrounds the urethra, it is quite possible that an enlarged prostate, by restricting the urine flow, can be a cause of UTIs . I believe this would be more common than a UTI causing the enlargement of the prostate.
On the UTI, it is so important to give extra water till the infection clears up. I give water 4-5 times per day with some tuna in it to encourage extra drinking. this is almost as important as the antibiotic. they always have free choice water, but giving the water with an incentive in it, can increase their water consumption almost 100%.
BTW UTIs do not show up on blood tests, and they generally do not raise the temp until quite severe. I have had lots of these with 5 handicapped pugs. They are very prone to UTIs as I have to express their bladders manually, and this is not as efficient as nature. Once you have this bladder infection cleared up, if I were you, I would pick up some chemstrips at a pharmacy, and keep track of Blue's urine ph, and blood content for a bit till you are sure the prostate is not causing the problem. I find that most often, the urine ph wil increase (more alkaline) before the blood appears, or the bacteria can be seen under a microscope. this gives you a real jump on any problem.
So glad Blue is doing better.