Nursing home placement when only a minimal amount of funds are available?

Personally I wouldn't wait for another fall. Call 911 now, tell them she fell a few days ago and now is not acting like "herself". No reason to wait.

I agree with all who stated call 911 to take her to hospital and if/when they try to discharge her please do not take her home. Get social worker to help you place her. If you take her home the process to place her will be more difficult and longer. Insist that she cannot return to your house as it is unsafe for both of you.

Hospital staff, primarily social workers will need to do their job and help place her, where both of you will be safe.

Best of luck to you.

Next time she falls, you call 911 and have her transported to the ER,(even if she is ok after her fall, you can say that you think she may have a UTI or has had a stroke, even if it's not true)and while there you tell the hospital social worker that your mom is no longer safe in your home and that you can no longer care for her.
They will then have to find placement for her, and Medicaid will have to be applied for.
Now those at the hospital will try and talk you into taking your mom back home with lots of promises of what they can all do for you. DON'T believe a word of it as none of it will be true.
Just keep saying that you mom is an "unsafe discharge" over and over if you have to, and they will get her placed for you.

I think that with the next fall I would call EMS.
They can transport her to the hospital for xrays or whatever.
There you should contact social services at once.
If you are her POA you should let them know you cannot accept her back into the home because you are unable now to care for her.
This will start the placement.
Begin to gather together all facts about your POA if you have one, her diagnoses, her assets. They will need this to start placement.
If her funds will soon run out then you will need to tell them she will require placement in a facility that can accept Medicaid, and perhaps help you apply for it when it is necessary.

Next time she falls call 911, have them transported to the hospital. While she is there meet with the social worker and tell her what’s going on and you can’t safely take care of her anymore and she needs Nursing Home care. While she is there, apply her for LTC Medicaid. Tell the SW she needs to go to a nursing home while Medicaid is pending. Then follow through with state Medicaid, providing them all the information they need, bank statements, etc.

Why don't you call 911 and have her checked out? Tell them something's going on with her health. She may have a UTI or stroke, or something else. She needs a diagnosis so that you can help her make further care decisions.