I have rather large lumps on top of both feet. They are hard and very painful. When I tap on them they send tingles across the top of my feet.?

See a Podiatrist. Unless we can see them is difficult to know what could be. One possibility is lipoma (growth of fatty tissue). Other possibility neuroma (a growth of a nerve). I cannot rule out fluid from congestive heart disease, or other conditions. My suggestion...Go to see a foot specialist (podiatrist).
Ganglion cysts. Gangion cysts are caused by tears in the tendon sheath or joint capsule allowing lubricating fluid to escape and fill up like a balloon. In certain locations they may put pressure on nerves which cause shooting pain and tingling. They can be aspirated however they usually return unless surgically removed.