Hey Dude,
I served an LDS mission but did not know I was celiac at the time. I was aware tho of milk allergies hypoglycemia and here's how it went:
The MTC was very accomodating. The head cook knew me well and would make me any dish I wanted or buy me anything from any store/ health food store and have it ready by whatever time I asked him to. He set aside a shelf in the kitchens where I could access the soy and rice milk he bought for me. This was pretty amazing as there were how many thousands of missionaries there he had to take care of...
The mission was ugh.. ..could have been a lot better if I had known what I was up against (celiac). If I had known, I would have made arrangements with members who cooked dinner for us to cook gluten-free or simply bowed out of dinners and cooked for myself. WHile I enjoyed getting to know the members over dinner, it wasn't worth the price my gut paid, if you know what I mean. I went stateside so we had dinners scheduled EVERY night. The RS was usually more than willing to accomodate any food prefferences or allergies in the English wards, but in the Spanish speaking wards/branches, the folks were generally less educated about ingredient lists and food in general ("but it's NOT wheat Sister, it's white bread, see?").
My husband went to Russia and they never had a meal cooked by the members because the members were so poor. You would need supplemental $$$ from your family tho bc eating brands you can trust (there's no FDA in Russia

is expensive over there.
My point is, you can do it. It's just a matter of 1.) being educated yourself - what can you buy for yourself, how to prepare, or eat straight from the can, etc.

2.) educate your bishop, and stake pres. Specify your special needs on your papers before you send them in. Stake Presidents are allowed to make recommendations for where to send you based on stuff like this. 3.) Get to know the head cook at the MTC. If you need to, also educate your branch pres at the MTC. Wives of the presidency enjoyed bringing me food from the Outside World now and then. 4.) Educate your mission president and comps. That ought to do it. Oh, and don't be afraid to stick up for yourself. If dinners with members are still getting you sick despite your educating everyone who'll listen, graciously cancel all dinners at members' houses. Be sure to visit them anyway, just don't eat there!
Good luck!