You don't mention ice. Are you doing that? I think ice is essential for reducing swelling, inflamation and pain, and for preventing further injury.
I know Tuli cups come in two sizes. I tried the larger and it pushed my heel up so high, it cramped my toes. My shoe rubbed the back of my heel. I can't image how any woman can wear high heels and not have all kinds of foot problems. Anyway, I got very good relief of my symptoms just wearing cross trainers that sound a lot like your new jogging shoes. I think your doctor should check the fit of your shoes, with and without the Tuli cups.
Can you wear your jogging shoes when you teach? I hope so. If you feel hesitant, explain to your principal. Try teaching sitting down as much as you can.
I think getting completely o.k. again takes us all a long time and requires patience. But I don't think you should be patient with getting worse.
Good luck. Please post if you find an explanation for why you got worse. Other people will probably go through what you're going through.