Is concave lens is used to cure short sightedness?

No, a concave lens is used to cure long sightedness not short sightedness.

A concave lens is a type of lens that causes light rays to diverge (spread out). It is used to correct farsightedness (hyperopia), a condition in which the eyeball is shorter than normal or the cornea has too little curvature. This causes light rays to focus behind the retina instead of on it, resulting in blurred vision. A concave lens diverges the light rays before they enter the eye, so they focus on the retina instead of behind it, correcting the farsightedness.

On the other hand, a convex lens is used to cure shortsightedness (myopia).