This has been going on for three years?? I”m so, so sorry. It sounds like a sad and lonely way to live. I’m very glad you wrote. This has gone on far too long.
I can’t make a diagnosis on the basis of a letter. I can only tell you that your subject line may be right: It sounds like maybe a combination of social anxiety and depression. It may also be that your dad’s expectation that you are to assume the mantle for taking care of the family should he die is causing you more stress than you think. But the label/cause doesn’t matter. What matters is that you are becoming more and more isolated.
It’s way past time for getting some help for this. If you could have solved the problem yourself, you would have done so long ago. You are missing out on college experiences and the kinds of friendships and memories that are the foundation for lifelong relationships. You aren’t making the connections that will help you when you graduate.
Most schools have a mental health service of some sort. You might start there. See what they have to offer. If there isn’t such a service, ask you doctor for a referral to a therapist who also has experience with family therapy. I’m guessing that you may eventually need to have a few sessions that include your dad.
You made an important start by writing to us. Now please follow through. You’ve missed enough. You deserve to find your voice.
I wish you well.