Betty has likely been bitten on the face and has developed an abscess.
This is an accumulation of pus and blood under the surface of the skin.
While it can be dramatic when it ruptures and there is a visible hole, this is actually good, as it allows the infection to escape.
However, given the extent of the lesion and the fact that there is still discharge, it looks like Betty is not able to deal with this infection on her own.
She does need to see a vet who will flush the abscess and prescribe some antibiotics and anti inflammatories so it can heal.
While less likely, we also need to consider that it may have been caused by e.g. a rotten tooth or foreign body, so these would be checked for too.
Do continue to clean her cheek at home and you can also protect it by keeping her indoors and having her wear a buster collar.
For most, they will heal rapidly once medicine has been started.