I agree with everything that savior said.
I get this problem too but I only get this problem when I'm coming down with oneitis =/.
And about that looking twice thing, I think we humans have a tendency to "double check" because we're a curious bunch and maybe she's thinking the same thing as you too which would probably explain why her friends were looking at you (she asked/told her friends this guys looking at me, does he like me?(just a guess though))
Before I broke up with my gf and lost my nuts, one thing i did that was fun with eye contact was that I used to make faces (funny) at a girl that seemed like she was looking at me, just to see if she reacted and if she did i would talk to her and so on
P.S. If you guys could give me some advice too on my post It would be greatly appreciated
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