Unfortunately, I've had several from running, so you have my sympathy. I don't think you should rule out plantar fascitis, either. Not that that's a picnic, but you can do some stretches that will help with it.

If it is a fracture and I'm any indication of how fractures heal, it can take anywhere from six weeks on. My worst one (recently) took three months. Good luck with your recovery. I hope it's a speedy one.