Probably no. You can claim a deduction for medical expenses for medical care you provide to a parent who you could claim as a dependent, meaning you pay more than half their total support. If three siblings are providing help then probably no one is providing more than half your mother's total living expenses.
If the 3 siblings together pay more than half your mother's support, and if your mother has less than $4050 of taxable income in her own name, then one of you can claim her as a dependent if you get a signed multiple support agreement from the other two siblings. You might rotate this around from year to year. Then, the sibling who gets to claim the dependent for a given year can claim the medical expenses paid for your mother, including expenses paid by the other siblings, because that can be treated as a gift from the two other siblings to the third sibling who then pays the bills.
However, medical expenses are only deductible when they are more than 10% of your income, or more than 7.5% of your income if you are over 65. So the expenses will only be partly deductible at best.
Then, the nursing home expenses might not all be considered qualified medical expenses depending on why she is there. This is what the IRS says,
You can include in medical expenses the cost of medical
care in a nursing home, home for the aged, or similar insti-
tution, for yourself, your spouse, or your dependents. This
includes the cost of meals and lodging in the home if a
principal reason for being there is to get medical care.
Don't include the cost of meals and lodging if the rea-
son for being in the home is personal. You can, however,
include in medical expenses the part of the cost that is for
medical or nursing care.
