Not much has been said here, so I thought I'd at least say something, although I don't know a cure.
My fiancé picks the skin around his fingers and began picking his hair too. He has lovely hair and his hands are already a mess so I've been trying to make him stop...
Usually you have to notice that you're doing it to keep yourself from it. He does it when he's feeling self-concious or stressed. When he does it I tell him not to do it and if he still does I hold his hands. But that doesn't work for everyone
You probably just need something to do with your hands. When I'm nervous I have to do something with my hands, and when there's nothing to do with them I pick my nails. You need to so something besides picking at your hair. Try really hard. Tap on something, doodle on your hand, stuff your hands into your pockets... Wear a hat that covers your hair and make a vow to not take it off until you can do so without picking. (or just take it off and put it back on once you realize you're picking)
As for eyebrows, if you're home and aren't easily embarassed, put tape or bandaids over them.. That way when you reach up there will be nothing to pull.
Eyelashes.. I wonder how you manage to do that, it's painful. You need to not do that and just be very aware of your hands, keep them down at all times.
You probably do this because of stress, learn relaxation techniques or go to a therapist and see if that helps.
That's all I can think of, good luck.