Where do I start to get my elderly sister into a nursing home without the help of doctor?

horton72, more than half the battle is won since your sister wants to go into continuing care. What are her health issues?

If it is within her budget, she could easily go into Assisted Living. One doesn't need a doctor to do that. The Assisted Living will access her needs to see if she would be a good candidate for the facility. Please note, such places average around $4k a month depending on where she lives.

If your sister needs around the clock skilled nursing care, and your sister refuses to go to a doctor.... then the next time she falls or doesn't feel good, call 911. That way she goes to the hospital, then to rehab, then into a nursing home. Would your sister be self-pay as nursing homes on average are $10k per month, or would she need to sign up for Medicaid [which is different from Medicare]?

Why does she want to do this without the help of a doctor? A doctor has to attest to the fact that she needs skilled nursing care.

If she doesn't need that, she can find and assisted living facility to live in.

Take her to see her doctor and explain the situation. If you have already tried this, find another doctor.