When sores/scabs (miliary dermatitis) are concentrated around the cat's neck (and/or at the base of the tail, under the neck) it's often allergies. Still, even though the pattern may not be keeping with usual ringworm symptoms, it could be this fungus.
If it is ringworm (a fungus, not actually a worm) - yes, you can try treating it with what you'd treat human Athelete's Foot. Just use ointment and not a spray - finding the med in your anti itch aisle. Be sure it says 'treats ringworm' on the label. If this doesn't resolve it about 5 days - you really should see your vet.
There could also be Cheyletiella mites on the body (rather than just in the ear).
Eosinophilic Granuloma Complex (it has other names too) is known to cause scabby sores on cats. This is an immune system related disorder/disease and though the sores look more like raised, scabby scratches (with hair loss), this is not always necessary to make the diagnosis.
Finally, Feline Leukemia and/or Feline Immunodeficiency are known to be found in conjunction with scabby, persistent skin disease. If the cat hasn't been checked for these viruses, it's important that they are. While a long and uneventful (health) life is possible, certain precautions need to be taken, diet modifications are probably necessary and regular vet check ups will become part of all of your lives.
To explore more about possible causes and even options available: http://www.peteducation.com/article.cfm?cls=1&cat=1332&articleid=150
Nutritional modifications may help - just as you imagine it would. This link is by a specialist who offers some amazing information and includes home recipes you can try for your companion http://www.catinfo.org/
Putting things on your cat (other than trying the anti-fungal ointment for a week or so) isn't suggested. Unlike humans or even dogs, cats ingest most of what's put on them because they are instinctively fastidiously clean.
They have different metabolisms - different systems. What might make sense to put on us for dry scalp can make things terribly worse for a cat.
It could also be a side effect of thyroid disease.
There's just so much that causes this symptom it's really worth it to have a vet take a look and figure it out right from the start.
Good luck and keep up the good job with her!