Will a burst blood vessel in the penis heal itself?

In almost all cases, yes it will. Ice pack it for the first day or two -- ice 10 minutes on, 10 minutes off, a few times a day. If there's a lot of pain, any distortion in shape other than minor swelling, or any occlusion to the urethra, or anything else that worries you, call for a medical consultation -- otherwise it'll heal by itself.