My husband has mild allergies to peanuts and tree nuts. When he was little they would give him hives; now, he'll get a headache and more congested than usual if he's sitting at a table with an open bowl of nuts for a while, but he's eaten a couple by mistake and nothing's ever happened to him.
It is possible to have a hereditary allergy to nuts. You could ask your pediatrician to run an allergy screening to avoid a potentially dangerous reaction if you think your child is also possibly allergic. I THINK that the first time you eat something, you may not have a reaction, it is subsequent exposures that pose the threat, although you may want to ask your doc.