How To Treat Pain And Swelling Of Thumb As I Slipped And Fell Down?

I slipped & fell on the ice outside my house last night. My left palm, at the base of the thumb bruised immediately. A few minutes later it started to swell. Ice & tylenol helped the swelling, but it's still a little swollen & bruised. It felt ok when I woke up, but the longer I was up the more it's beginning to throb, like a dull stabbing pain. It is tender to the touch at the bruised area & around it, at the base of my thumb in the palm area. Should I go get it x-rayed, or is it likely just a sprain?