If she is not on oral antibiotics, she needs to be. If you feel Gangrene has set in, this needs immediate attention, which I would have her seen in the ER, as treatment of the dead tissue needs to be done as well.
Here is a site you can read more on this too Click here
I don't know the protocol of the nursing home she is in, but you should find out what course of treatment she is getting for this.
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Healthcare Expert
17+ years, Healthcare Expert