Depression Support Group
Depression is a real and debilitating condition that is often misunderstood by family and friends. Its meaning can range from a prolonged period of sadness to an actual mental illness with specific symptoms. Find and share experiences with others who are going through the same struggles.

Look beyond your classes, I know you're quite busy but invest time in just one club where you think you might find people you can get along with. The hour or 2 of invested time will help you perform better because the isolation won't weigh on you.
It takes time. Keep being friendly. Invite them out, and find a school club for yourself. Those are the best places to start.
I moved to a new state and spoke to no one. It took one girl to reach out to me. And it wasn't easy. I only gave her one-word answers. We became best friends, I visited her in Boston and if she would say anything about me, she would say,"When I met Soul, I couldn't get her to talk. Now I can't get her to shut up!" lol
If I'm anything I'm an extroverted introvert. I need my me time but I also want to see friends and do stuff together.
I think shyness is there for a number of reasons: fear of rejection, a natural inclination toward introspection, to name a few. If it's the first, it can be overcome. It's scary at first but it takes practice. You didn't get to be a musician by waiting for someone to force you to play. You chose to play. You can also make that choice in your own life. Try talking to the other shy kids around you. They will appreciate that you came up to them and it could lead to a great friendship for both of you.
In short you have to learn to accept your self and your solitary life, and see it as your foundational point, become secure in it and happy in it, and then you have to quietly branch out and grow from there. And as you grow from there, friends will happen automatically, as a byproduct.
Don't be jealous of the people you see. You see their faces. You don't see how they feel inside. Just do you and let them come in their own time. :)