Theres small tiny red bumps on my hand. only on the back side of my hand not on any other skin. is it possible that hand soap caused it? i accidentally used a hand soap as a hand sanitizer without water for two days. but only one hand has, why?

If there's no itching an allergic reaction or contact dermatitis isn't likely but still possible. I would expect both hands to have an itchy rash with an allergic reaction. It could be a primary irritation eruption from harsh detergent and/or vigorous rubbing of that hand. You could try applying a mild corticosteroid ointment. See your physician or a dermatologist as needed.