Have you ever power puked? On the times in my youth where I um, over-indulged alcohol to the point I projectile vomited, I'd often get strawberry patches around the eyes (granted not on them). Same kind of deal when you get a surface mark from the bar on back squats or similar stuff. It's really probably no biggee.
I mean, if you get to the point where your eyes are completely bloodshot all the time, you might want to take it easy on the handstands.
Also, could be diet related?