The cause of pain can be anything ligament tissue or bone injury, u need to see an orthopaedic consultant near u to examine ur hand and know the right reason for ur pain. Beside u also need to give rest to ur hand for atleast 3 weeks. Pain and swelling is the result of the injury and it will be there atleast for a month if no major issue. Onoy if the swelling and pain is out of proportion then its a concern. Good u used ice only post injury.  Use creepe bandage.