Since your son is allergic to a Hymenoptera or bee stings, he is at risk for having an allergic reaction with future stings. This includes wasps, hornets, yellow jackets or honeybees.
Mosquito bites usually cause local reactions and rarely would cause an anaphylactic reaction.
He can continue to camp outside while taking precautions. This includes wearing long-sleeved clothing, bug spray, and having his epinephrine available. Your son should have an anaphylaxis plan with instructions on when to use epinephrine.
I would recommend that he be evaluated by an allergy specialist for skin testing to different Hymenoptera venoms. Venom allergy shots (immunotherapy) might be an option. This treatment could lower his risk of an anaphylactic reaction after a future sting.