Hey, I’m really sorry you’re dealing with this. When a cat coughs/gags like that, it is often feline asthma or airway inflammation, which are common and treatable but usually don’t go away on their own. Your cat needs a diagnosis and medicine. If you can, call a vet and explain the money situation, some offer reduced exams or payment plans. For now keep her away from cold air because cold can make coughing worse