Check out vegan cookbooks for non-dairy ideas; many include gluten free recipes too. Some vegan recipes use dairy replacement products, like soy milk, while others make do without, so both of those methods might appeal to you.
I drink a lot of dairy and eat a lot of gluten, so I can’t help with specifics, though I can point you towards some vegan recipes that I make. What type of food do you like? Some of my favorite vegan recipes involve a can of tomatoes, some type of beans or chickpeas, and spinach. Stirring in some hummus gives it a creamy quality without using dairy. Serving with corn tortillas is really good too. I made something the other day that was basically tomatoes and black beans, with eggs cracked over the top and baked until the eggs were cooked through. You can easily add some chicken or sausage or some other meat to most vegan recipes if you want.
Did you get tested for these allergies? I’m just curious, since I have a lot of allergies, but thankfully no food allergies.