My brother says that his feet felt that way after he dropped a cheeze pizza on them (bare, of course)(the feet, I mean). He had to go to the hospital because of the burns. Perhaps in your case, dropping a cheese pizza on your bare feet would get the circulation going? Extreme measures, I know. But at least you'd be getting lunch at the same time. :^o

You can get (and almost definitely will, should you live to be 80) some neuropathy with or without diabetes. My totally nondiabetic mother (I say totally because we've checked her numbers a lot) has a lot of neuropathy. The good news about diabetic neuropathy vs nondiabetic neuropathy is that diabetic neuropathy tends to be reversible, especially at the beginning.

Have you ruled out other causes, such as insect bite or allergy?

Allergy? I am incredibly allergic at the moment, but I've never heard of that affecting the feet...?

That sounds scary, I hope it goes away soon   

My toes get sore/numb/tingly when I hike/walk in shoes that are too small, even if they don't really feel too small when I put them on.

Allergies kind of affect everything, so it could be some sort of allergy.....Once, I had problems with my hands AND feet due to a reaction to something, but I am also considered borderline or prediabetic, so who knows?