Read Timothy McCall's response:
Years ago, I had a bout of plantar fasciitis, so I have some idea of what you must be going through. As the -itis suffix in fasciitis suggests, the fascia on the sole of the foot is inflamed, and that's why your doctor has prescribed prednisone, a powerful anti-inflammatory drug.
When an area is acutely inflamed, it needs to rest. Too much activity, including too much yoga, may only makes matters worse. A hot room temperature also tends to promote inflammation, so I would avoid practicing in this kind of setting for the time being.
In addition, I would recommend you avoid any poses that cause pain in the foot. Focus on seated poses, prone backbends on the floor, supported inversions, and relaxation poses. Breathing practices, chanting, and meditation are all fine. If your teaching requires that you to demonstrate poses that aren't good for you, you would be better off either not teaching or simply calling out instructions while someone else (perhaps one of your more advanced students) does the demonstrations.
Take this opportunity to teach your students a crucial lesson: Explain to them that ahimsa, nonharming, is the foundation of yoga, and that right now you need to take care of your injury, which is why someone else is demonstrating the poses. Doing so may give them the permission they need to take care of themselves and refrain from potentially harmful poses when they've got an injury. Once the inflammation has cooled down, poses that stretch the soles of the feet and the calves could help you recover.