How long would a small, kind if deep ,about half a centimeter, take to heal whithout anystichesits been 3 weeks already?

Skin laceration: If your wound is still open it most likely is infected and that is why it has not closed up. You might need oral antibiotics or topical antibiotics to help it heal. It is too late for stitches, and the wound needs to be cleaned out so it can heal by itself. Ask your provider to teach you how to keep it clean so it can heal properly.