You are exhibiting mild forms of depression due to the fact (as you explained) that you feel lonely. I dont think you need anti-depressants.

What I see more appropriate here is that you learn how to express yourself and communicate. It seems like you have those friends because they came and talked to you. The good thing is that you seem to be a nice and charming person that when people come and talk to you you dont behave inappropriately or tell them to get lost. You are a likable person once someone gets to know you.

It seems like you might benefit from like communication training so that you don't let that anxiety you feel when you are with other people take a hold of you. You are viewing yourself negatively in this respect, you are judging yourself by the amount of friends you have. Dont be so judgmental of yourself. Relationships come and go but you have to deal with your social skills to approach people instead of them approaching you all the time.

I don't believe you need any anti depressants. These are issues that can be fixed without medication.

You say you have friends in school, but don't see them after school? I agree, this can make someone feel a bit lonely. Why should you wait to be invited somewhere? I spent most of last summer at home because no one invited me anywhere. But then I got with my more outgoing friend, and started events, like inviting a bunch of people to the movies. I think you could try that. Instead of waiting to be asked to go somewhere, suggest to the friends you have in school. It's not like you are asking complete strangers, they are your in school friends, and you are just expanding your friendship to outside of school.

And you said yourself that you need to take a chance and talk to people. I know that the self esteem can be a hard thing to deal with, but it is what you said, a chance.
Think of it this way: You are lonely and sit on the computer at home. What can be worse than that? You have nothing to lose by taking that chance and talking to people.
And I think if you do that, you'll meet girls, and then you'll get the chance to find a girl you may be interested in asking out. It's all about that first step and taking the chance by talking to people. If you still have trouble with it, whether your shy at the moment, or it's the low self esteem, think that you don't want to stay where you are in life right now. You can solve it. Think of that for that little push you may need right when you are about to talk to someone.

Good luck, hope this helped a little.