Man ive been there, it's tough for sure.
Im not sure how great you'll take my advice, but this is what helped me....
The problem with how you're living right now is that by in large you are undesirable. That's not a personal dig, nor an assumption, but rather a truth in which your whole life is based on.
At twenty, you're at the age when relationships are a big deal, but you're not really projecting a lot of desirable qualities.
It tends to be a downward spiral. You feel life your life's empty so you try to ask out people, then if you get rejected you feel shattered, then you begin to feel depressed, this then counters your desirability even more as you'll be projecting a lot of negative energy.
The good news is, you don't have to live your life like this. The bad news is there's no easy fix.
What I did... Was I went away and worked on myself, and I did that by doing things, things I'd not done before in my life. I told myself, ok for the next few months, don't get caught up in hot guys and girls, just concentrate on yourself.
And a few things happened.
Firstly I became a lot happier. By a lot, I'm talking un-quantifiable measures here, my life went from sitting in front of the tv/laptop thinking I could never be happy, perhaps I was just built this way, to jumping out of bed in the morning and not hiding behind the sink at the sight of my reflection.
I also became more aware of relationships. This was a big one. I became aware of the importance of good friendship, and the qualities that come with non-judmrnt, compassion and companionship.
We live in a world where sex is everything, if you're not doing it whilst bungee jumping of mount Everest and landing into a submarine before being air locked into a cargo plane and flown to a tropical island you might as well give up.
But as a by-product, of a society in which sex is the be all and end all, we lose important irreplaceable views on relationships.
I can't tell you how liberating it is when you dont view every interaction with potential lust or expectation, but rather mindfully enjoy the bond in itself.
Lastly of course, the main thing was I became more desirable. I became an interesting person with actual things to talk about.
And these are all things you can feel too, you can be happier and you can get girls, but you have to start with yourself first, make yourself happy, don't place your happiness on the validation of others and people will become way more interested, plus you will be more confident, which will improve your life tenfold.
Anyhow that's the theory.
As for the practical.
Firstly, ask yourself if there's one thing, a hobby perhaps, that you've always wanted to try, and go force yourself to do that.
Or, alternatively choose a few things and try them out! But above all force yourself. Dont be that guy at 30 wishing he had not wasted his 20's to anxiety and fear.
For me, I started Muay Thai, I got serious about my religious practices (completely personal choice here) I began to meditate every day, to use mindfulness, to have compassion.
I also joined the gym, took up a language, studied topics I'd always been interested in and began to plot a career path.
I dont even go to Muay Thai anymore as I can't afford, but the confidence from that alone Still fuels me.
Anyway, my fingers are aching as I've had to type all this on mobile, I'll update it later perhaps, but hey, even if right now you don't feel like taking this advice, I hope one day it will of use to you.