Red spots on the hands may have several causes. Examples of these are contact dermatitis, dishydrosis, herpetic whitlow and fungal infections. In your case, we may have to consider dishydrosis and herpetic whitlow. Dishydrosis is non infectious while herpetic whitlow is infectious. Herpetic whitlow is due to herpes simplex type 1 infection. This may spread through direct skin to skin contact. This may resolve spontaneously but given proper triggers like stress and decrease in the body's immune (defense) response, it may recur and persist. As for dishydrosis, this may lead to an itch scratch cycle causing skin excoriations leading to dishydrotic eczema.
Are you applying any medications on the area?