I find fried/greasy foods bother me, but not spicy foods. I'm South Asian and grew up eating spicy foods (as a child, I longed for 'exotic' foods like tuna casserole and macaroni and cheese!) and Indian food is my 'comfort' food. The only difference has been that I can't add chilli peppers to my food as that messes me up.
As Dan says, turmeric is a good anti-inflammatory, and the masala which is added to Indian foods usually contain cinnamon, cardamom, fennel seeds, coriander, cumin, nutmeg, and black pepper. Indian food also has lots of garlic, ginger and onion. Some of these spices may react poorly for some people (I find that I can't add coriander to my masala mix as that has an effect on me).
I tend to drink chai (Indian tea) after dinner to soothe my stomach---the fennel and ginger that I add seems to really calm my stomach.