I need power of attorney to get mom medical care and into a skilled nursing facility. How?

Agree with above and Barb has best advice from my own experience. If there is not already a DPOA in place, then you can't draw one up or change after the fact especially if she is incapacitated. You have couple choices:
Involve APS and tell them you have no power. That means u have to step away and be willing to let them handle. Possibly do a emergency custody order to get her placed.
2nd. You file for guardianship and consevatorship over mom. Expensive and time consuming I'm told.

Fractured pelvis is painful, which is why the poor dear falls when she stands up as it probably hurts her.
Agree wth the above- call 911 and have them take her to the emergency room, that's probably the only way she will be treated.
Her GFR is very low. Starting to think about Dialysis occurs when the GFR is less than 15%.
She could be dehydrated too.
Talk to her PCP and discuss her condition with them as well. They may have input from a prior experience. 
Definitely have 911 take her to the ER as that should get the NH process started.
Good luck to you as I know this is very heartbreaking and hard to go through.

If she falls. Call 911. Do not go to her home.

Do you think the EMTs will leave her there, soiled and in renal failure alone? I doubt it. I believe they would be forced to take her to the hospital.

Do not meet her at the hospital. Let the medical professionals deal with her.

I know this sounds cruel and cold. But you cannot reason with dementia.

Dear Janie,

I'm so sorry to hear what you are going through. I know you love your mom and want her to get the proper care. Its so tough. Maybe consider talking to her doctor? Or a social worker? Or can another family member or friend help you take her to the hospital against her will? I feel like the ambulance has to take her because she is in renal failure.

Thinking of you.

You need the person involved to grant you Power of Attorney. Then the attorney drawing up the POA document is ethically bound to refuse processing the POA if they feel the person is not mentally competent to be making legal decisions.

In other words you face two huge hurdles- getting your mother to agree to give you POA, then finding an attorney who would draw up the POA in spite of your mothers cognitive decline.

Your best bet would be to seek legal guardianship. The guardianship process can be lengthy - especially if the principal or anyone else objects. It is also a bit expensive- however, if you are awarded guardianship the cost of doing so can be reimbursed to you from your mothers funds. In dire circumstances an emergency guardianship can be granted in a matter of days. 

Find yourself an attorney who specializes in elder care and they can asses your situation and advise you on the best course of action.

Not much you can do on your own. You might try area on aging for her county. They can come to her home and evaluate the situation. She might listen to them where she won't listen to you. If they find she is a danger to herself they may have her committed for further evaluation.