M.C.
I can only respond to the diet part.
I gave up all the dairy and milk to see if that helped and it didn't and on my own I found out that my baby quit throwing up her milk when I did not take my vitamin. I quit taking my vitamins and she never had another problem.
Everything does not come up when they spit up, unless maybe he keeps doing it, so as long as he keeps thriving and not losing weight, he should be good. You could look for signs that he is not dehydrated, like a sunken soft spot for instance. Any problems and I would not hesitate to call your dr.