Rabies is probably not likely. Most animals that can transmit rabies to cats transmit through bites. The most common animals are pretty large, and usually kill the cat while biting : foxes, dogs, etc. Although bats are definitely a concern in many areas.
Cats hide when in pain or sick. So, she could be hiding due to that. They try to avoid pain, problem is they don't know where the pain is coming from usually. They feel like their mouth hurts, and they know that, but they don't know what is causing the pain - IE my tooth is bad. I have seen dogs with tooth problems attack their feeding bowls because they think that the food
bowl is hurting them when they are trying to eat.
The strong unpleasant smell coming from her mouth could very well be an abscess, and most likely a tooth abscess.
If so, she will need antibiotics to clear it up, and possible sedation, and sugery to clean out the abscess pocket. Unfortunately, there are no medications that you can give at home that will fix that. I wish I could tell you there was.
You will need a visit to the vet on this one. And I think the sooner the better.
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