I have been having burst blood vessels, mostly in my hands. is this anything to worry about?

Yes it could be: See your doctor high blood pressure, low blood clotting, thining of the blood, central infections and many things. Even though it may just end up being varicosities see your pcp first.

Several Things.: The most common cause of veins bursting and bleeding in the hands would be trauma. Other causes could be the taking of blood thinners such as Coumadin (warfarin) but also nsaids, aspirin, fish oil, flaxseed oil, plavix, etc. Another cause could be blood problem resulting in an inability to clot. Obviously, it is impossible to make a diagnosis based on only a few facts. You should see a hematologist.