My 10 Yr Old Daughter Closed The Car Door On

My 10 yr old daughter closed the car door on her pointer finger. It swelled from knuckle to knuckle splitting in the middle from swelling. She has mobility and bruising. Little pain just tender when she touches things. The area that spilt is still puffy and her whole finger is considerably colder the the rest of her fingers. Is this something I need to address urgently? I'm concerned about proper blood flow with the coldness of the finger. Thank you for any help.