Can a UTI go away without antibiotics?

Possible. If the UTI is attacked head on with forced fluids and you have a good immune response, it is possible to flush out the bactreia in the bladder and the body wins the battle. I would not count on this. If you have burning, pain, frequency of urination, need to go immediately, and cerainly if fever, back pain, nausea, chills or vomiting, get seen right away for a proper diagnosis and treatment.
Possibly eventually. Not worth waiting it could take forever, ie may never clear up. Most utis eventually cleared up in the preantibiotic era, but some didn't. Please see your dr. Or nurse prcationer and get a prescription. Bactrim, Cipro (ciprofloxacin) and generic Nitrofurantoin macrocrystals are all fairly inexpensive, especially at walmart. Good luck.