May (in-grown toe nail) recur if cured, why? is it cured just by surgery or some medications may work ?

Matrixectomy: Unless the nail matrix (root) is removed, there is always a chance of the nail problem recurring. There is a difference between a nail matrixectomy (which is a permanent removal) versus a nail avulsion (which removes the offending portion of the nail but does not remove the root). Both procedures are in-office surgeries with local anesthesia. See a podiatrist.