Here are some things you should remember:
Lactose intolerance = You CAN USE LACTOSE FREE DAIRY PRODUCTS without any problems.
Milk allergy = You CANNOT USE MILK in any form. This includes following foods: cheese, cream, chocolate and ice cream.
Check out the following link just in case:
https://gluten.org/2019/10/15/celiac-disease-non-celiac-gluten-sensitivity-or-wheat-allergy-what-is-the-difference/