My sister started obsessively making this loud whistling, breathing sounds with her mouth that sound like a wave. She says it's anxiety?

Obessive mouth noise. This is a problem that needs medical evaluation. There are many possibilities including obsessive disorders, tourette's syndrome, movement disorders etc. Call her doctor for an appt. To be evaluated for the cause.
Mindfulness. Suggest books on mindfulness as they are a wonderful way to alleviate anxiety without medication.