What could cause burning inside the top of my hands off and on that leaves redness?

Likely dermatitis: This sounds like a contact dermatitis from a substance you're coming in contact with like a hand cream or soap or a set of gloves you are using. See your doctor or a dermatologist.

Possible allergy: Sometimes, one reacts to substances one comes into contact with during the normal course of the day, such as a soap or detergent. Such a skin reaction is termed a "contact dermatitis". If this seems a possibility in your case, try avoiding the offending substance or try using rubber gloves with a cotton inner lining. If it persists, see your dermatologist.