The inside of the hand is the palm. Make a fist and your four fingers will be touching your palm.
vola manus
The palm is formed from the metacarpals, the thin bones between the phalanges (finger bones) and the carpals (wrist bones).
The veins are closer to the skin.
Go see a doctor because that is not common at all... This could be an allergic reaction to a product such as dish detergent, soap, lotion, etc. that you've just begun using. Allergic reactions can...