His dairy sensitivity is probably just that, and you can more than likely start reintroducing it into your diet in SMALL quantities.... like maybe an 8oz glass of milk per day, or 1 cup of yogurt. I had to switch to Lactaid with my son, but yogurt, cheese, etc were all ok. He outgrew it about 6mo, but remember that babies don't have the enzymes in their digestive system to handle cow's protein easily until around a year (although some babies are more sensitive than others), and his gut is just now sealing all the holes he was born with.
Personally, I'd spit up rice cereal as well, regardless of what's mixed with it. Have you ever tasted it?? YUCK! My son had MAJOR constipation issues with rice cereal that went away when I switched him to oatmeal. However, you don't necessarily need to feed him just baby food. A good rule of thumb for feeding is to give him the foods you want him to eat as he's growing, so pretty much anything you eat, minus the large, hard chunks (apple, hot dog, popcorn) and anything that isn't recommended before 1 year (milk, honey, egg whites).
Spitting up could be a result of his reflux, or it could just be because he ate too much. Also, Dr. Jack Newman (world expert on breastfeeding) just recently said that reflux is now one of the most common diagnoses in babies, and it's not necessarily what's wrong at all! Just as we throw up things that our bodies can't digest, or something that's made our stomach upset, babies do the same, especially if they've had too much. Their bellies are much smaller than we think, and a 6mo will drink no more breast milk per day than a 1mo... they just drink a little bit larger quantities, less times per day.
Hope that helps!