First of all, no dog should be out unless they are on a gentle leader. Are you using a gentle leader to walk your dog? It gives you much more control over them. Second, you need to see a trainer. Yes, dogs can become possessive and exhibit guarding behavior. A certified trainer will be able to help you with this problem. I also wonder about illness since this has kind of come on all of a sudden. YOu may want to take your dog in for a check up as well. Right now, at home, your dog should be on a leash and with you at all times. He/she has lost the right to be free to roam the house right now.
As for exercise, if you feel your dog needs a bit more than you can muster up to give them, then get a used treadmill and walk the dog on it. It is not very hard to train a dog to walk on a treadmill. Both of mine do it. Again, a certified trainer can help you with this.
JGF gave you good advice. You do have to be careful as an aggressive dog can be a liability issue! Trying a Gentle Leader may be a good idea but you will have to be vigilant knowing your dog may be aggressive.
Consulting a trainer is a good idea.
Read up on NILF dog training.
Try to avoid letting her have eye contact with other dogs.
Also, has she had a bad experience with another dog?
Is she spay?
Vet check and blood work is a good idea and ask that her thyroid be checked.
Good luck and please update
You need to consult a canine behaviorist ASAP. Your dog is a mix of two breeds that have both been bred to display aggression toward other animals. It is dangerous enough to have an animal-aggressive small dog, but when a breed with the strength and tenacity of a pit bull is involved in the mix it becomes a real liability. You have the makings of a real problem on your hands so please don't waste time trying home-grown solutions, get with a real behaviorist as soon as you can.