I have mouth burning when I eat bananas too; google oral allergy syndrome. I didn't know what it was until I found out my sister in law had the same thing; something to do with a pollen reaction. She can't have apples, either. I get a burning mouth, sneezing and runny nose with cucumbers, bananas, and I'm afraid to try avocados because when I use skin care products with it, I break out in a painful rash.
FWIW I've eaten cucumbers in chopped salads before because I didn't want to waste the time sending the food back, and all I got was bad hay fever and a burning mouth, no serious allergic reaction. I think this kind of reaction is pretty mild and not the same as a dangerous food allergy.