Diaper rash = allergic reaction??

DD ate carrots last night for dinner. She pooped today and immediately got a diaper rash. This is the 3rd time this has happened. It's only with carrots. Is she allergic?? She has no other reaction, just a rash as soon as she poops after eating them. That's kinda random to be allergic to :-/.

Also- I'm allergic to pineapple (it suuuucks because I LOVE pineapple) so is she more prone to being allergic too?