Why is it that after i had a bloodtest in my arm i started to feel the vein move?

Vein/needle did move: Most likely you felt movement induced by both a combination of the needle & your response. Larger veins are below skin, not fixed to skin and can move; allows our skin/body to move with differential stretching/compression. The vein can easily slide sideways in response to the needle tip, esp if not very sharp, or esp if aimed a little off center; more common. Good phlebotomists work to compensate.

Phebitis: In order to draw blood, the vein was entered with the needle. This local trauma by the needle can make the vein irritated...Phlebitis. A small blood clot or thrombosis could also be at the site. Leak of blood around the site can also cause a small hematoma. Treat with NSAID meds like aleve (naproxen) and heating pad or warm moist heat. If the pain progresses, seek physician review.