not sure what you mean by "too fizzy". it is a carbonated beverage and, since it will have more body than, for example, Bud or Corona, there will be more head.
Never seen Bud claiming they're wheat free. think you're getting some misinformation there. only some beer (like Glutenberg) are gluten free (i.e. wheat free). if Bud is using pure malt extract (which i sort of doubt is the case) then, sure. a physician recommending beer? also doubt that. Bud doesn't give away their recipe, but most, if not all, beer use 2-row or pilsner malt as the base malt. Bud uses rice (cheaper, ferments out) in addition, not as a 100% replacementl
http://www.wheat-free.org/wheat-gluten-free-beer.html
there is absolutely nothing there that suggests that Bud is wheat free (and gluten free)