First boo boo

My DD got her finger caught pretty badly in our baby gate last night.  My husband was closing it and didn't realize her finger was in the gate.  Last night it was red and swollen behind her knuckle.  I iced it and gave her some tylenol before bed.  She 's moving it and doesn't seem to be in pain but her finger is still just as swollen and red this morning.  I was hoping the swelling would have went down on its own last night.  Any suggestions on how to con a 1 yr old to sit with ice on her finger?   I gave her a teething ring to hold onto... that was the only idea I had.