Pain after having blood samples taken from the arm. Negligence?

Probably not. Negligence? Every time something bad happens does not mean its someone's fault. A small amount of temporary pain is common. You could have some inflammation called thrombophlebitis. Also, a venipuncture is a minor procedure and all procedures have risk. Injuries to arteries, nerves, or muscles are very uncommon but possible. If it persists please let allow the md who ordered the test evaluate it.