My name is***** and I am sorry to hear that Mimi is coughing. Coughing in dogs can be caused by many different things including collapsing trachea, allergic airway disease, pneumonia, kennel cough and others. Before I can recommend a treatments, we really need a diagnosis. I would strongly consider taking her to the vet if you can.
The cephalexin that you were prescribed is way too much for a tiny dog. I do not recommend giving it to her.
You can try Children's Benadryl liquid. The dose for her size is 1mL (about 1/4tsp). This is the only thing safe over the counter.
I know you also said that you have financial concerns. Do you have a local humane society near you? They often have a full service veterinary hospital open to the public that is usually less expensive than general practices. You also can consider Care Credit. This is a health care credit card that you can use for yourself and your pets. Lastly, the ASPCA has an entire page dedicated to folks who want to help others with their vet bills. Check that page out at https://www.aspca.org/about-us/faq/financial-help-my-vet-bills.
Best regards, ***** ***** this answer helps you.
Feel free to contact me if you have any more questions.
Kansas State University,
College of Veterinary Medicine Class of 2001