Thanks for using JustAnswer.com, I'm Dr. Dan and I'll try to help you.
I am concerned about your kitty mainly because you are right, cats are very clean animals and usually do not let themselves smell poorly unless they are sick. I am concerned that she does in fact have a UTI as infected urine can often smell very strongly and a small amount on the skin can smell very bad. I also worry about urine scald, some cats who have either normal or infected urine and do not clean appropriately can have severe skin reactions and infections from the urine. This can smell like urine an actually be a painful skin infection. She won't usually act differently unless the affected area is touched which is why urine scald infections can go on a long time before their noticed. I know it's no fun to spend money but I think a urine evaluation and a physical exam are a really good idea before small problems turn in to big expensive ones. I hope this helps, best wishes.