It is normal to get burning in your eyes when you use prescription eye drops to treat your eye allergy. However, the burning should be temporary and it will go away later. If you get burning eyes all the time, you should go to see a doctor as soon as possible in case there are some other serious problems with your eyes. However, make sure you follow the doctor's advice to use your prescription eye drops.
If the eye drops burn your eyes, the eye drops may not suitable for your eyes. You shall stop it. You shall consult your eye doctor to get eye checked. I usually heard that people get allergies with eye drops may feel burn and pain. And your eyes are allergy as you stated, so you may look for prescribed eye drops from eye doctor you give your an eye check. S/he know better about your eyes that will give your the proper eye drops to help you.
Actually, I have to remind you that you should never count on eye drops, you also have to give up some bad habits that give rise to your problem, besides, you are supposed to pay regular visits to your eye doctor who gave you medical treatment, you might as well get professional advice from him. Good luck!