Hi, thanks for using healthcare magic
The pain and swelling would be related to the soft tissue injury
to the muscles and tendons in the hand.
Icing it would definitely be helpful.This should be done 3 to 4 times a day for 10 to 15 minutes
In addition you may want to consider the following: (1) resting the area as much as possible
(2) compression bandage to reduce the swelling, it may also help with the pain
(3)elevate the hand ,this would also help with the swelling that you are experiencing
(4)anti inflammatory pain killers such as aspirin, ibuprofen
.This would help with pain relief and also aid in reducing the swelling
If your symptoms do not improve in 24 to 48 hours or worsen , then you should consider visiting your doctor for an assessment.
I hope this helps