I don't know if I look stupid.

I don't know how important is eye contact while talking to people, but not only girls, I cant hold it.

I feel inferior, I feel I know what people is thinking about me and seeing all my flaws and judging me so I just look away while talking to them, probably looking so dumb or insecure.

Two situations happened today :

1- I was at a bar , crossed eyes with a girl who kept starring me (you know when someone is looking at you) I tried like two-three spaced times to look at her and hold eye contact just to try to see what happens (maybe she just was thinking about how ugly I was, or how stupid the shirt I was wearing looked) no matte what she thought, I wanted to see what happened to the end of the eye contact, feeling like it was a duel between the two but I couldn't hold it more than a second and look away.

2- Second one I'm with my father and we come along this hot milf he knows, she says I was at her work place a few days ago, and I realized I couldn't watch her to the eyes, I kept looking at my father and hold eye contact to her like one second max back and forth.

Give me all kind of information about eye contact, is it important? What are any tips I can use to being able to hold it? Does it lead anywhere? Am I wasting my time?

Thanks