it's going to be developing the awareness of anything that might remotely have a chance of containing any kind of peanut substance.
And it will be fairly safe to assume that you have the same awareness for any kind of nuts. We took our oldest son to the hospital three or four times over the years for anaphylactic reactions to nuts, all but one without him even knowing that he had eaten anything with nuts in it.
It can be very scary. You're going to have to keep epi-pens around all of the time now. One at home, one in the car and one in your wife's purse. If he is cared for by babysitter(s) then one with them also.
Good luck, stay aware and all of that.
Our oldest son finally outgrew the peanut sensitivities when he was in his thirties but is still highly allergic to tree nuts.