Tie the arrows to a line - do that you can find it if it doves into the water?
Btw, just having my morning coffee. Came home empty handed... One boar showed up, but it was still too dark to shoot.
Discussion
Yes, so it doesn’t escape and suffer. Since alligators are cold blooded they are very hard to kill. They have a lot of residual nerve/muscle activity even after you sever the spinal cord as the law requires. Shooting with bow/airbow/harpoon only catches it. Then you have to finish it off with a point blank high caliber shot to the back of the head and then cut the spinal cord then ream out the brain with a tool to make sure it is dead even before taking it out of the water. Even still they are known to bite after all that.
Here’s hoping you have better luck next time and definitely post photos. Even what you do with the bounty. I just started learning about charcuterie and want to go hunting for wild hogs again if I can.