My mother owns a hamster, but she is allergic to soybeans and all of the hamster foods in the store contain them. We want to be able to keep the hamster, but anything that contains soy puts it into the air and makes my mom cough. There are soy-free foods for humans, so surely there are some for animals, aren't there? I'm worried, because my internet search didn't find anything, but maybe someone has some knowledge I lack.

I think it's quite impossible to find soy-free hamster food on the net. You can try going to your local pet stores and ask around, but it would be much of a search in vain because hamsters are born to eat everything nuts, beans and veggies.

The thing is, other than the dried pet food, they can consume a wide variety of vegetables. You can try to inhabit more green diet into your pet, but must not totally stop them from eating the dried food as they provide essential vitamins and stuffs for him/her.

Also, leave your hamster in a well-ventilated place, and allow the particles of the food to go out of the house and not circulation the room.

Hope it helps.

Try this addy and click on the "soy free" link as Tami has all kinds of info and may be able to help you with a soy free diet, though she has rats but strongly believes in a soy free diet.
http://www.socialrats.com/