There could be numerous reasons for small bumps on your skin. Red bumps are probably pimples, acne or bug bites. Reddish bumps could also be caused by a razor. Small white bumps could be cysts or whiteheads. Other causes could include treatable skin conditions such as eczema. If you don't know the cause, determine what might have recently contacted that skin.
Check all around your body for bumps. If they're near stubble on your legs or face, change your razor blade and use a more skin-sensitive shaving cream.
Wash the bumpy area regularly with a mild cleanser for two or three days. If the bumps go away quickly, they could have been bug bites. Clean your bedding and clothes.
Use bar soap meant for sensitive skin, such as Dove, for a while to see whether it helps. Your soap or lotion might have caused the bumps.
Use sunscreen or long sleeves and pants outside. Reduce your time in direct sunlight.
Continue to keep the area clean and don't let the bumps contact oil, grease or dirt. See a dermatologist if you think the bumps are pimples or if they persist or worsen.