3 yr old woke with tummy ache, went potty later, diarrhea, ate a bite of breakfast, threw up, feels better/feels sick, lethargic, no fever. ?

Gastroenteritis: While these symptoms certainly sound like a viral gastroenteritis illness, she could have food poisoning or a few other more concerning illnesses. If she is lethargic, I am concerned and advise you seek medical help asap. For right now encourage electrolyte based fluids (pedialyte, gatorade, etc).

Stomach virus: It sounds like she has a stomach virus. Start with small amounts of clear fluid (Pedialyte or watered down Gatorade). If she tolerates that for 2-3 hours, gradually add light foods- crackers, toast, dry cereal, applesauce, bananas. If she keeps vomiting or has fever >101, check with your doctor.