Why does cheddar (all varieties) give me stomach ache but other cheese such as mozzarella, colby jack, etc. Do not?

Cheese. The difference may be in the formulation of the cheese. Cheddar to give its texture and consistency uses lactate which can cause stomach bloating pain gas etc. mozzarella and other cheese doesn't. Perhaps try lactaid pill (contains lactase the enzyme that beaks lactate down) prior ingesting your next slice of cheddar. Hope this helps.