How do you eat healthily if you have an oral allergy syndrome?

Depends on allergens. The food that causes oral allergy syndrome varies with individuals and what pollen they are allergic to. In most cases, cooking the vegetables or fruits will destroy the protein causing the reaction, and the food can be eaten that way.
Depends. It really depends on the raw fruits and vegetables you are having to avoid. There are probably some fruits and vegetables that you can tolerate. You should also be able to eat the fruits and vegetables that bother you as long as they are cooked.