Does my dog have a UTI?

It is possible, but I would wait a few days and see how things go. If you notice that the frequent, abnormal urination continues take him in and get some antibiotics. Watch him over the next few days and see how things go. FYI - the food you have him on is fine; the number 1 cause of food allergy is chicken, not 'grain.' Many people have misconceptions about dog food and the only difference between expensive and less expensive foods is the quality of protein.