I believe I have issues with Casein. I haven't been tested for it, though. I do have Celiac disease as well. I have tried lactaid pills and lactaid milk and they did nothing for me. This is why I think it's the milk protein and not lactose. I can tolerate a little bit of goat cheese or goat milk but I can't do it regularly. I have tried eating organic fancy hard Irish cheddar from TJ's - one bite is okay, but any more and I feel sick So I've just given it up completely instead of tempting illness.
For me, dairy leads to immediate nausea, and then a "blah" feeling all day, and depending on how much I ate I get constipated.
If your intestines have been damaged by an immune response to Gluten, it is highly likely that you are lactose intolerant and will be until your intestines heal. This is because the little villi that are damaged by a response to gluten also happen to be the ones that break down milk sugar. Often people with Celiac report that once they are gluten-free and have completely healed (this can take months, or even years) that they are able to eat dairy again. I personally was diagnosed last November so it's been about 6 months and I still have problems with it, another reason why I think it's Casein and not lactose.
Did you get tested for Celiac? If not, you should. It's an easy blood + urine test that will be confirmed with a scope. Remember to eat gluten a bit before the testing date so that there isn't a false negative.