I used to have that problem growing up because I had allergies with post nasal drip. In the mornings my stomach was often very queasy. If you think your son might have allergies ask about putting him on a daily antihistamine and nasal spray to see if the problem gets better. I also found it helped sometimes to eat a few saltine crackers right away when I got out of bed, before I walked around much, and then wait a half hour or so to eat anything else.
Yes, you should discuss it with his pediatrician and likely have your son evaluated by a pediatric gastroenterologist.