Blood vain blowed in top of hand for no reason and really burned is this a normal thing?

Veins: The skin of the back of the hands is very thin and sometimes a tiny venule or capillary bursts from minor trauma, being on aspirin, aleve, (naproxen) blood thinners, etc. Unless you're having frequent events of easy bruisabilty, blood noses, bleeding gums, etc. There is no need to worry about an occasional bursting of these tiny vessels in thinned skinned areas like the back of hands or forearms.