Good news on the diabetes front. To answer your question, it's possible you could have a UTI and not know it - I did.

I have a hyperactive bladder due to the MS so had to see a urologist earlier this year. Having to stand round a water cooler with a load of geriatrics drinking a litre of water because the bladder refuses to perform is slightly bizarre...

Anyway, as well as being complimented on the excellent tone of my pelvic floor (!) they found I had a urinary infection too - dunno why, nothing was staying in there for very long!

I'd had no symptoms - no burning sensation, nothing.