No. This isn’t “normal”. It certainly sounds painful. It sounds to me like you are so discouraged about your ability to connect with people that you have given up. You justify it by convincing yourself that you don’t want to “burden” people. But it is more likely that you have lost your own confidence about how to interact with people. I’m concerned that your relationship with your boyfriend is going to suffer if he is the only person you are comfortable with. That puts a lot of pressure on your relationship.
I concerned about how depressed you are feeling. If that doesn’t abate, some individual therapy might be helpful.
It’s very difficult to solve problems with social skills by staying alone. You can’t think your way out of this. Ideally, I’d like to see you in a group therapy situation. Group therapy provides a safe place to talk about your issues and to practice interacting/communicating with others who are going through the same thing. You will give each other feedback and support while you make changes.
If you are unwilling or unable to get into group therapy, please consider getting involved in some kind of sport or club or volunteer work that will keep you in touch with other people in a way that puts the focus on what you are doing more than on each other. That will give you more experience with more kinds of people until you feel more socially comfortable.
Please follow up and get yourself into a group and/or activity.
I wish you well.