Lactose intolerance and being allergic to dairy products are very very different things. It is a good idea to figure out which problem you have.
You're lactose intolerant, allergic to dairy products. I developed this same allergy and had to completely eliminate dairy from my diet or I would get sick. Yes it *****, but you have to listen to your body. Look at it like this - someone with a fish or peanut allergy avoid those foods because their body will reject them and effect the body negatively. Well, that's what dairy does to you. Eliminate dairy products, it's not worth possibly developing digestive problems just because you want that slice of pizza. Good luck
Welcome to the gastroenterology community! It sounds like you figured out the solution to your problem. Just avoid all dairy (milk, cheese, ice cream, yogurt, butter, etc.) and you'll be fine!!