I think you shouldn't wait and you should go the doctor and get an Xray and preferably an MRI. It is either broken, fractured or something was torn such as a ligament. You don't want it to set wrong. An orthopedic surgeon would be best but it depends on your insurance as you may have to see your family practice doctor first. There may be some nerve involvement because of the way it is spreading around. Since the palm of the hand it is getting cold you really need to get some help.
let us know what happens.
mkh9
It's possible you could have cracked a bone, especially with such extreme swelling. Icing on and off (20 min. on maximum and then a break) and taking ibuprofen or naproxen (not tylenol) will help with some of the pain and swelling. If it turns bright red and you see red streaks going up the arm, go to the hospital because that's a sign of a major infection (although I don't think a thumb injury would be at all likely to give you one).
I wouldn't use that hand while it's swollen. If it's a comfortable angle, put a little gauze in between the thumb and first finger and then tape them together, or tape around the hand if the thumb isn't long enough to stay in place. You're splinting the thumb against your own hand. Padding is important, to keep it dry and from creating too much pressure, and if it hurts, don't do it. You can also put down some gauze, put a popsicle stick on it, and then wrap to the popsicle stick as a splint. Again, take it off if it hurts, and change it if it gets wet.
It could be anything from a sprain to a torn ligament. I would suggest if it is not better within 7-10 days after the incident to go get it checked. Best wishes, Sissie