You poor thing. Can you get the kids in a casual day at after school care? I know ours often lets people do that in an emergency.
If you go private it will be exxy- DH had an arthroscopy and some cartilage removal on his knee about 6 ys ago and we had PHI and we were more than 1K out of pocket. I would wait for public if at all possible, the cortisone injection may help for a while anyway.