Suddenly my mom got red scratches like (look like a scratch that didn't bleed) in her face and in her nose and under her eye. Is this symptom bad?

Probably not. Could be rosacea, dry skin that she has scratched, telangiectasia, pet scratches she should see a dermatologist.
See a doctor. My concern is that this may be the start of shingles ( a viral infection), and if so, it may affect the eye. If the "scratches" are all on one side of the face, this is suspicious. A doctor as soon as possible is in order.