Let me first say that what that women did is unconsciousable!
I think it best to bring him to a veterinarian ASAP. If you can't afford emergency veterinary care bring him to the your regular, non-emergency veterinarian on Monday with full knowledge that you may be putting your dog at risk due to the delay. It is difficult to assess damage long distance but is sounds like he has a fractured nose/muzzle, and a concussion. Dog
I think this is a bit more than a run-of-the-mill nosebleed. The dog may have crushed sinuses and a concussion, or worse. I understand your need to watch the money but this needs medical care. The neuro symptoms and continual bleeding is an urgent situation. Please take your pet to the vet ASAP. You probably don't know who the woman is but there's a good chance she could have been charged with animal abuse. Breaking up a dog fight by pounding one on the head with a rock is not really acceptable.
Read your own post. It seems that whenever someone describes what you described, and seems very fearful the dog will die, they should bite the bullet and take the dog to emergency right away.
It is the responsibility for every pet owner to provide adequate veterinary care for their pet. In fact, it is the law. If you do not seek care for your dog, who has apparently suffered a severe head injury, you are guilty of animal cruelty and neglect.
I'm sorry to sound so harsh, but it is extremely cruel to allow an injured animal to suffer and perhaps die because you don't have the funds to provide care. Many clinics will work with you on payments. Don't walk in announcing you have no money. Get the dog some help first, and then discuss the dollar issues. They'll have no choice but to work with you then, and your dog will have gotten the care he deserves.
I hope you made a police report. She had no right to do what she did, and she needs to be punished.