Is this normal or should I seek professional help? I have 3 internal (hit a vein) stitches and 16 external stitches to my left arm. I have a sensation of running blood or liquid going up and down my arm depending on the position. Is this normal?

Simple. Simple answer, you had stitches put in so you should have follow up, so yes seek help. Jjsut because you had stiches in a vein and elsewhere you should know however that that feeling may not be something you noted before or may be due to swelling. Whenever you hang your arm down the veins "fill" due to gravity. Moving your hand and forearm muscles actually helps to compress the superficial or surface veins, and the veins in the muscles and aids in returing the blood back to your deeper veins and ulitmately your heart. So it "can be" normal. ....But call the person you are supposed to be seeing for follow up and talk to them. If you dont have a follow up visit call the place where the stitches were put in and ask where to go.
With. With all due respect I have a hard time understanding what you mean. Please be more specific.