Veterinary services are never free. Someone always pays, whether that be a charitable institution, or the veterinarian themselves. Nowhere will offer you veterinary treatment for free, but there may be low cost clinics in your area. There are many options for possible financial assistance; a list of options appears on the website of Cascades Humane Society near you. I understand there are valid reasons why someone might not be able to afford veterinary care, and in such cases it is incumbent upon the owner to decide whether they are in a position to continuing to provide care for their pet. If that is not the case, then re-homing your pet may be a reasonable option.
There are any number of things that could be wrong with your cat, and it is impossible for anyone to give you a diagnosis online, or recommend treatment. It could be something very benign. It could be something very serious. Given your cat got outside and possibly fought with other animals, my major concern would be that she has a wound that has become infected. You can evaluate the skin yourself to see if you can see any puncture wound near the grey discharge. If it is infected, it is unlikely to resolve without veterinary care.
Given she has never been vaccinated and escaped the house, your cat may have been exposed to and possibly infected by a number of infectious diseases. Rabies must be considered since she is unvaccinated and is thought to have fought with other animals of unknown vaccination status or wildlife. Rabies is a serious disease. In an unvaccinated cat who may have been exposed to rabies, the Michigan DHHS recommendation is euthanasia, or if the owner refuses then rabies booster with 4 months of quarantine, and serologic testing. The severity of these recommendations reinforces the importance of vaccination.
It certainly sounds like your cat needs veterinary care. You can call the veterinary clinics in your area to ask how much it costs to have an appointment.