I'm having nose bleed after head injury but not hit in nose, normal?

Depends. "Head injury" doesn't mean the same thing to doctors as it means to laypeople. But practically speaking, whenever you have an unexplained nosebleed you should have it checked out. The blood may be coming from behind your nose. And even if it's coming FROM your nose, the nasal septum is supplied by 3 arteries, so whatever the cause, you can lose a lot of blood if it's not controlled.
More detail. Tough to answer w/o more details. A nose bleed after a head injury is not especially unusual, and may indicate a skull fracture or CSF leak. CSF is usually thin and watery, but can be blood tinged too. If the bleeding persists beyond an hour or so, call your doc or seek out an ER. Are there any other symptoms? If so, you might want to go sooner (bad headache, nausea, loss of consciousness...)