Yes. 3 days if you do the following
Keep taking NSAIDS (unless the swelling increases and becomes painful then consult a doctor/clinic)
Apply the ice pack to your palm (put it on the table and hold it like a mouse with the other 4 fingers raised) for 20 minutes at a time and never longer than that.
Use icey-hot, on your wrist, palm and on the back of the hand twice a day.
Heres where i make an assumption, eat better and take a multivitamin (centrum).
Awhile ago (11 years Jesus Christ) I was on a pro circuit team that got pretty damn far, Vegas far. Trust me when I say handling a controller for 10+ hours a day every day will cause permanent damage.