Even strictly indoor cats can get fleas so ruling that out would be first. (We can bring them in on our clothing/shoes etc... or visitors can bring them if their pets have fleas, or if she recently moved they can be left behind by previous tenants or the eggs can lay dormant for months and then hatch.)
Then I would check the food, many cats can develop food allergies which main symptoms are skin irritation. The major allergens in food are grains, fish, chicken, dairy and beef. So if your mom is feeding a lower quality food that could be the problem.
And of course it is best to consult with a vet, especially if there is hair loss. They have a history on the cat and can administer a shot or meds if the skin irritation and hair loss are bad.
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“The greatness of a nation and its moral progress can be judged by the way its animals are treated” -Mahatma Gandhi
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