Do you have a therapist? If not, now might be a good time... because what you are describing is the very sort of thing a good cbt therapist is ideal to help with. That's because the problem isn't really that you can't but that you believe that you can't. I mean, truthfully, you can walk into a doctor's office without assistance, in a literal sense... but the thoughts and feelings about doing so make it seem impossible. A good therapist can help you look at why that is, what to do about it and how to gain that independence you are now wanting.

Congrats by the way on seeing that dependence and wanting to change it - that's a huge and positive first step!

Another thing to look at are anxiety resources online, and a specific book my own T recommended called The Anxiety and Phobia Workbook. You'll find that your fears, etc., are not uncommon, you aren't weird or alone in this. Others have made it through it and so can you.

The suggestions about trying to take on a bit more while your sister is still here is also valuable. Think in terms of little steps. If you think about the big things it gets to feel like too much. Break everything down into the smallest steps possible - be ridiculous about it - and try to reward yourself lavishly when you complete any of them successfully. Don't give up when you don't get it right the first time. Keep pushing yourself to keep trying because if you pull away the world gets smaller and smaller. It will probably hurt and be scary but remember, it is fear that stops you and not any real lack of ability... and fear can't really hurt you. Being brave is being afraid and doing it anyway.

Find intermediate steps... like maybe find friends that are willing to go along as passengers in the car, or places you can tag long to just to be out more... you can do this.

best of luck - stay brave!