My penis is chapped when i get an a erection the skin splits open on the skin what could be wrong?

Are you circumcised?: Tight foreskin or phimosis can certainly split open with erection & would indicate need for circumcision. Splits likely heal with some scarring & thus wouldn't respond to prescription strength steroid cream. Suggest you consult a urologist. Also if UR already circumcised. Or you could email a picture of your erect penis for our comment. Such pictures remain private & secure.