Yes when you have an upset stomach bananas are good to eat when you have the upset stomach.
When you have an upset stomach you should eat what is known as the BRAT diet which consists of Bananas, Rice, Applesauce and Toast.
Hence the name BRAT diet.
So you can eat bananas, apples, applesauce, rice and even toast when you have an upset stomach and are not feeling well enough to eat other foods.
Just eat the foods slowly and if you feel like throwing up still then just stop eating and wait it out.
As long as you're getting enough fluids you can go a few days or so without eating food.
Sometimes when I have an upset stomach I cannot get any food down for at least a few days but when I can eat I eat bananas, and some toast or applesauce.
They are all healthy foods to eat as well.