Honestly, you're gonna hate what I have to say, but if you feel like you "can't give it up" there's a really good chance that you (and the baby) have a problem with it. Seriously--- dairy (and wheat) are addictive (google casomorphin addiction: dairy addiction) and are hard for a lot of people to give up even though they are causing them harm (even if it is "just" dry skin or minor eczema). It is much easier for people who truly have no problem with dairy to give it up. If your husband (who knows your eating habits and probably sees some of the effects of food) has also suggested it, I'd suggest giving it a try. It is difficult, but if you can get over the withdrawl period, then you'll probably notice a difference in how you feel (and how the baby is reacting).
Secondly, what do you consider a "true allergy" Do you mean IgE (ie allergies that can cause anaphylaxis--then you may be right, but many babies are affected negatively by foods. Reflux is a symptom often caused by food problems (dairy, gluten/wheat, soy . . . ), oversupply is another :-/ Screaming at night means the child is troubled, if he sounds like he's in pain, I would guess it is in his tummy, you can ease his symptoms, but until you find what is causing the problem, he will probably continue to be uncomfortable.
If you decide that you want to give a serious attempt at giving up dairy for your son, PM me and I'll hook you up with a support group of MANY mothers who have gone through it and in some cases are still struggling with it ;)
**reading your earlier posts, your son sounds EXACTLY like my daughter did around that age--turns out she had a soy "allergy" (and to make it worse I have dairy problems :/ that were causing oversupply.) Cut both out of my diet and it was a totally different child (as a plus her BMs got better, she was less gassy and I could actually make some dinner for myself and sleep for more than 6 hours.)
(A previous poster said that allergies don't manifest themselves as behavioral, but in reality they DO. People seriously go off for no reason if their stomach is bothering them. Chemical imbalances can throw off perception and comprehension. etc. Borrow "Is This Your Child" for a overview on some ways allergies can affect behavior.)