I would take it easy, and find ways that you can stay fit with the least amount of exercise.
Tell your Allergist you really need to be able to exercise to be healthy-we all do-and that you can't just keep an epi pen on hand "just in case".
I have heard that exercised induced anaphylaxis generally occurs when you exercise after eating a food you are sensitive to, so maybe just exercise on an empty stomach?
Ask your allergist but if he/she is not giving good enough answers, see someone else.
I know how panicked you must feel, I am the same only with eating, not exercising.
I really hope that you find someone that can alleviate your fears.
I would also suggest starting out gradually and building the exercise up. Don't just run a marathon-lead up to things. It's never agood idea for anyone, allergy-ish or not, to just exercise hard and fast.
Good luck and God Bless. :)