Son pinched arm over vein with a toy. It is red and swollen similar to a bug bite. Could the vein be damaged? Do we need to go to er?

No. Very unlikely. Veins have a fair amount of elasticity and it takes a very hard blow to an already weakened area to hurt the vein without breaking the skin.
Skin injury. This just sounds like an injury. If he can move the arm, has minimal pain or no other symptoms you can wait this out. If the arm cannot move or the spot that is injured is rapidly expanding you need to be seen.