This summer you need to go travelling. Since you are usually alone, I suggest you join a group with lots of young people your age like this company:
Travel Europe, Australia, New Zealand, USA, Canada, and Asia — Tours for 18-35 year olds — Contiki Tours, do a tour that lasts at least a month.
By being in a large group of people day in day out, you will familiarise yourself with these strangers and learn to talk and interact with them. You won't feel as much pressure as in a party etc. where you only have a short time to talk to people. And if you feel like running away, you can't because you are stuck for a month with them anyway.
Learning to interact with strangers is not just a way to meet girls, but is a life skill that will help you succeed in the future. Given your description of yourself, your failure to find a job after the first BA might have something to do with your shyness too. That situation likely won't change, unless you change. Even if you can get a job after this CS degree, being reclusive will curtail your chances of success, unless you are a genius.
I had a friend who was desperately shy like you describe yourself. We would sit at dinner for an hour, and he would say no more than a few words, and only when I asked him questions. I would try to find things to say to him and he would look up about to say something and then just give a nod and that's it. It's excruciating for the person trying to talk to him. Me, I never had any problem talking to strangers, mostly because I don't really care about making them like me, though I'm still nice and friendly. Since I don't care, there's no pressure to impress and conversation comes naturally. When I can't have a natural conversation with someone, I knew we likely weren't gonna be friends so nothing lost there. You need to look at talking to strangers as nothing to lose, since if you don't talk to them, you still have no new friend.
With regards to relationship, I think your problem is that the people who take the time to talk to you, and thus who you will likely feel attracted to, are the nice older ones who see your shyness and feel sympathy for you (sorry if that's a bit harsh). The younger ones your age are busy being chased by confident guy your age or older ones. If you want someone your age to go out with, you will have to work up your courage and actually talk to them.
But relationship isn't everything. One could be unhappy in a relationship and very happy without one. I liked being alone very much because everything I do, I only needed to please myself, but being with someone at the right time has its perks too.
Dr Phil said something very illuminating on TV the other day, to paraphrase: our society is so sold on the idea of coupledom, a lot of girls will do anything to be with a guy, even if the guy is abusive, rather than being alone. This can apply to a guy trying to be with a girl he's unhappy with too.
Oh, and my shy friend, he now has a beautiful girlfriend, a good job and have opened up quite a bit. You can have all those too.