Can you get your pilot's license and pass your medical exam if you have Severe food allergies?

I have severe food allergies, enough where my allergist requires me to carry an Epi-Pen and Benadryl as a back-up. I only ever use these medications if I come into a food that I am not supposed to eat, as I am not allergic to any environmental substances. Benadryl, I am sure you know is a medication that makes you a little drowsy, however it really doesn't make me really all that drowsy. EpiPens, if used, you are required to go to the hospital. Since I am required to carry these, and because of the way they react and the way you have to react to the medications, I am wondering, are these a disqualification to getting my medical and student pilot license? Thanks! :)