If he has a tree nut allergy it would only take a very small amount to cause a reaction. Two of my kids are allergic to peanuts and tree nuts. For them, eating a nut causes hives all over their bodies, itching, and vomiting.
However, if a person is allergic to nuts, their reaction may worsen to anaphylactic shock at any time. If your son ends up being diagnosed with a nut allergy, he should carry an epinephrine shot (the "epi-pen") with him. My oldest has never needed his, but it's with him at school every day, and his teachers know it's there.
Though a couple of my friends have relatively mild allergies to tree nuts, I know nuts in general can be a pretty severe allergy. They can even get worse and worse with each exposure. My friend's son was allergic to EVERYTHING and had to carry an epi-pen with him everywhere. I felt bad for him, because he had to bring his own food and cake to birthday parties and I could tell it bummed him out (even though I would try my darndest to make sure everything was allergen free - at least it lessened his chance of accidental exposure.) But when he was 5, they tested him again, hoping he had grown out of them and he did! Except for eggs. Still incredibly allergic to those.
One weird thing I found out though was that my friend has to give him peanut butter regularly now - at least once a week. Apparently it is a childhood allergy that you can outgrow but it can come back if you aren't exposed to it.