I'm thinking of letting my undiagnosed anxiety sabotage potential budding relationships.
What exactly do you mean when you say "undiagnosed anxiety?"
I'm always having a lump in my throat when I talk to people
You should never let a mental health issue go undiagnosed. It's always a good idea to overcome your anxiety.
I don't want to overcome my anxiety. I really want to be left alone and I think studying is better for me.
Even if you want to be alone, eventually you will have to interact with people. It would not be good to have to deal with your anxiety for no reason. It would be better to seek help so that you can feel comfortable talking to others.