I think I burst the vein in my palm when I fell... My palm is almost completely instantly purple, but no pain. What can I do about it?

Can close palm? If you can fully close palm without pain, then there may be only blood in skin, however you may have broken bone which should be ruled out. To speed resolution of blood in skin bormelain orally can help..If the are is swollen with a hematoma a physician can drain area if necessary.
Heat, compression . The bruising will go away with time. Heat may help it clear faster. Try soaking your hand in hot water (not hot enough to burn) for 10-15 minutes 3x a day. You can control the swelling by using an edema glove.