I am by no means a medical professional, but I do have a similar reaction to being in grass or around furry animals. Mine is just an allergy, and they either settle down on their own or with the help of an antihistamine. That might help your son! But like I said, I'm not a medical professional. Good luck!
It looks like hives which come and go in response to an allergy. You can give him some antihistaminic like benadryl or Claritin. Although the bite may be itchy, avoid scratching it because you may damage the skin, and allow bacteria to get in, leading to infection. You may also need topical and oral steroids which are available under prescription. Also try to find the offending allergen (grass, dust, plants etc) which may be causing this allergic reaction.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.