Ringworm takes weeks to respond to treatment, so that may be why it was not helping. It can be a combination issue as well. So you all can get treated - at least have one of the affected get a culture. ie you at your doctor/dermatologist or your friend or the cat at the veterinarian. Ensure a sore that has not been treated with anything at all gets cultured or you may get false or partial results and then have poor success with treatment or recurrence. Depending on the cause, each one involved may have 6-12 weeks of appropriate meds needed -- ie the earlier someone gets tested, the sooner you'll see results. Once one of those involved gets an answer, the rest should see their medical providers and inform them, so the best course of action can be taken - should also help devise a way to prevent reinfection.
Yuck! I've gotten ringworm before from patients (cats), and it is usually self-limiting (because the ring worm belongs to a different species - animal, not human), so thankfully it typically goes away in 2-3 months. That said, it can spread and is highly contagious. I agree with Dr. Mathis - bring that cat to a vet for treatment, and you to a dermatologist. I wouldn't put any neosporin on, as this can make it worse (you're creating a moist, wet environment, which is exactly what ringworm loves to grow in - after all, it's a similar fungus to athlete's foot or jock itch). You can try an anti-fungal cream (Tinactin, etc.), but we'd really recommend that you consult a human-doc on this first! Good luck!