This morning I accidently hit my arm while closing a minivan's door but I didn't feel any pain then, now it hurts....Could it be broken?

Possible. Possible broken but most likely a bruised muscle. If the pain gets worst or you loose motion you need to see an orthpaedic surgeon.
Probably not. If you didnt have immediate pain, it is unlikely that you fractured your arm. More likely a contusion.