Hi
@Lizdrizzi and welcome.
Are you Gluten and dairy free through intolerance of them, or is it just that you feel you are healthier without them?
T2 could well be re-named Carbohydrate Intolerance. Carbs are the only macro nutrient we don't ned to eat at all.
Whenever we run low on carbs(which almost immediately turn into Glucose, the body starts making glucose from protein for the small amount which is essential to our brain. In fact for the most part the brain functions well with Ketones as its main fuel.
So take a look at seriously cutting down on sugars and, starches as contained in fruits, grains and root vegetables.
Meat, fish, eggs and leafy green veg are healthy for all T2 diabetics. Full fat Chees &plain greek style yogurt are good fro those who aren't lactose intolerant (though Lactose is a sugar so there is little to be found in hard cheeses , greek yogurt or double cream - there is much more of it in skimmed milk).
If the ethics of them don't bother you, then true nuts (not peanuts or cashews) are nearly all low carb as are certain fruits used as vegetables such as avocado, cucumber, marrow, courgette. Berries (straw, black, rasp or blue) are also low enough in carbs that most are OK eating them in moderation with either double cream or greek yogurt.