My mom has red spots and bumps on her face and neck and she says it itches and it stings. We've tried putting aloe (both bottled and straight from the plant) as well as ice compress. She has been taking ibuprofen to get the redness and swelling down.
What could she take or put on her skin to help cure or relieve the itching and the burning?

I would advise your mom to see a doctor.

There are so many rashes and different skin conditions, that it is not safe to assume anything.

Applying different without knowing what it is for sure creams could worsen the rash.