T.K.
I would see a pediatric allergist. Peanut allergies are very dangerous. You will probably need to carry an epi-pen for accidental peanut exposure (with medical follow-up). I have a cousin with a 2 1/2 year old who has peanut, tree nut and wheat allergies (among others) and they are managing very well. You just have to be diligent every day. Eventually it will be habit for you.
Also, a friend has a 12 year old son with both peanut and tree nut allergies. As they grow, kids are so adaptive, that they get used to being on the look out for their own protection. Whenever he is at my house, he and I always carefully read labels together before he eats a packaged snack food. He also knows how to use his epi-pen.
Good luck!
T.