You are describing a difficult situation. It can be nearly impossible to get someone to seek help if they don’t want to or are afraid to for some reason, and I agree, it sounds like your sister needs help. There are several approaches that you could try. Having a family intervention (and perhaps even include some friends) might be helpful if you can do it in a loving way. You can look up how to do these online, but the gist of it is having a planned discussion with your loved one about your concerns and have treatment options lined up. They either need to agree to develop a plan and follow through or there may be consequences, such as, cutting her off financially or refusing to socialize with her unless she seeks help, etc.
Other options might include you or your parents going with her to the doctor, or if you all share a family doctor, you can preemptively inform them of your sister’s condition and your serious concerns. Perhaps the physician can then address it the next time your sister goes for something medically related.
You can also reach out to your local community mental health center and seek guidance from them. Perhaps they have therapists who do home based counseling. Or you can see if there are any support groups in your area for depression and anxiety and offer to go with your sister to ease her anxiety. Here’s a link to a website in your country that may be of assistance as well: http://www.mifa.org.au/index.php/en/
Ultimately your sister will have to be the one to seek treatment and unfortunately she may put this off until her life becomes unbearable otherwise. However, it does not mean that yours has to be unbearable too. You need to live your own life and let her live hers.
All the best,
Dr. Holly Counts