Your son needs 2-3 servings of "dairy" each day--they don't have to be plain milk. Some people just don't care for milk. It's great he likes cheese!
Whole milk yogurt would be a great option--he would be getting all the benefits of whole milk then. Stoneyfield makes some really great whole milk yogurt. I think it is harder to find in regular grocery stores--you might want to check Whole Foods or a co-op.
You can try to make smoothies with whole milk as the base. Throw in some fruit that he likes and whip it up in the blender.
There are lots of other ways to get your milk besides "straight up": cottage cheese, sour cream, kefir, homemade mac 'n cheese, milk or cream based soups, hot dishes with milk in them, pancakes made with milk.....
IMHO, I think we've overestimated our children's need for straight milk. Kids often drink way more than they need to, anyway. I hear of families of 4 going through a gallon of milk a day--that is WAY too much milk for people to be drinking! The recommendation I've heard for toddlers is no more than 16-20 ounces of milk per day. That's the high end of the range; if they are eating any other dairy, it should be subtracted accordingly.
FWIW, my son is 15 months old, and he drinks around 8-12 ounces of goat's milk (he has issues cow's milk), mostly in the morning with his breakfast and morning snack. After that, it's plain water. He really didn't care for water at first, but we started out by diluting his milk, and slowly increasing the water. He does eat goat's cheese & yogurt.
Good luck!