Regarding this idea, we have multiple elements, each element changes the way a dragon's body is built thus changing the way they are supposed to be healed,
But keeping the main vital organs the same in some way.
Elementless
Removing the stuck arrows by biting it off
then lick the injured area a little bit then exhale some fire to stop the bleeding.
Electric element,
Any stuck arrows will burn by applying shortcircuit,
no need to apply pressure or anything, as the injured area will be welded together using positive and negative magnetic energy
Fire element.
Any stuck arrows will be burned shortly after getting the damage.
Glyde will Apply pressure on the injured area for a bit, you will see a fire similar to brass welding work.
Water element,
Any stuck arrows will slide out shortly after the damage, as fish have some sort of foamy material which help them swim faster underwater by reducing friction of water itself
Then licking the injured area to apply some thick material stopping the bleeding.
Nature element,
Removing any stuck arrows by biting it off,
Then simply laying downsleeping animation and the injured area will grow some branches connecting between each other and pulling themselves together and the bleeding will stop.
Wind element,
Use exactly the same as elementless animation
Earth element
Removing any stuck arrows by biting it off
Then lay on the ground and biting or grabbing any material from the ground and put it on the injured area and apply some pressure and it will heal it.
Ice element,
Freeze stuck arrows after receiving the damage and it will break and fall, and the area will heal immediately.
Regarding none arrow damage
Glyde will lay down and exhale ice towards the damaged area and it will freeze the injuries stoping the bleeding.
Crystal element,
Any stuck arrow will be burned by lazer,
Any injured area will grow crystals connecting eachother and a lazer to cut excess crystal
