What kinds of things do you do outside of your mum? Do you go to school? Work?
I'm a lot older than you, and will be devastated when my mom dies - I think that's true for a lot of us. But I'm sure your mum would want you to be okay after she dies - which hopefully won't be for a long time. Since you're young, how about now starting to find some friends? You can take your time, and slowly get to know people.
Are you and your mum in therapy? I would suggest not going together, but it would probably really help you both. Find a young counselor, maybe, who understands BPD and being young today.
Your mum can still be your favorite person, and she probably always will be - that's awesome. But she needs to be able to care for herself, and you need to know that while you would be very sad without her, you can survive. I imagine she'd find peace knowing that, too.
So start small. Start figuring out what you like to do, and find a group that does it. Maybe start online, and then do it in person. Maybe it's politics, knitting, fandom, arts, music, sports - whatever it is (and I'm older than 22, so my examples probably suck lol), you'll figure it out, and go from there. Maybe you can help your mum do the same thing for her own interests. She's depressed, but there is help out there for her, too.
Oh gosh, I can relate. I was very close with my mom as well. I wasn't married in my 20's and this was my whole 'family'! I understand this. I would think that working on the mental health portion of this problem would be essential. A psychiatrist may be of great benefit. Medicine can do wonders especially when paired with talk therapy. Cognitive Behavioral Therapy is very beneficial. If the anxiety over potentially losing her is suffocating and impacting your daily living, this is important to get a handle on. And medication and CBT may help with the social anxiety and general anxiety as well so you can add a few more things into your life. Encourage your mom to do what she can for her own health since you say she is in poor health. But you take care of yourself as well! What is her health condition?