I also do the staring thing! It kinda freaks me out when I do but sadly I have kinda got used to it. Part of the anxiety I have been dealing with for 15 years. I know exactly what you mean and it's hard to explain. Try not to worry too much about it, I know, easier said than done
Also, if you are worried about the vision problems you could see an eye doctor just to check things out!
Hope this helps a little,