Allergies not only come from breathing air but all kind of material you can get in contact with. I got an allergy in Singapore noone could find the reason of. I also had to take cortisone drugs and anti-histamine. After leaving the place, everything stopped after a year or so.
You could also get allergies from local food. Chances are that you get new allergies in places where you never have been and your body never has been exposed to.
The only way you could find out is to try it! Go have a vacation there and you will see. At least in the short term.
I wish you good health,
Dani