Panties + Wrong detergent = UTI?

Is it possible to get a UTI from using the wrong kind of laundry detergent? As in, let's say, one you've recently found out you're allergic to? I have a very mild allergy to this detergent my parents just bought. We still have our old kind, I was just using this one for the first time and I've used it to wash all my clothes and bedding. I started having severely itchy eyes and sneezing constantly. I rewashed my bedding and my eyes are better but now I keep feeling like I have a UTI even though I drink tons of water and I'm using cranberry juice too. I don't have a fever or blood so I haven't seen a doctor yet. All I'm asking about is if the detergent could be causing this because it's starting to get painful and I'll be seeing my doctor soon for meds but I don't want to take them if the problem will reoccur anyway