Red dots all over stomach do not itch or burn?

Petechiae. What you describe sounds like petechiae which is the red pinpoint spots (1-2 mm) that results from intradermal hemorrage (bleeding under the skin) from small vessels in the skin. The red dots/spots can look like a rash, are usually flat to the touch, and don't blanch or fade when you press on them. Petechiae can be a sign of a number of conditions that can be serious, so please have it checked.