Can I jog on a no-running profile, or am I stuck walking everywhere?

Most likely stuck walking everywhere. I got put on light duty once and was told I couldn't run. But everyone knew I ran everywhere. I eventually had people watching out for me to try and catch me running. Threatened to write me up if they caught me running again.

I get it, they're only watching out for me and want to make sure I heal properly. But it can be frustrating when you're really motivated and want to train hard. So be careful.

Unless it says something along the lines of "run at your own pace" you can't run, unfortunately.

Sounds as if you have access to a pool. They may have ‘running vests’ that keep you upright while you are ‘running’ in the deep end of the pool. There are a number of workouts you can do that will keep you in shape for running, but keep weight off your knees. From time to time I’ll have an injured XC runner do such exercises—anywhere from 3-6 weeks—and they get a pretty healthy workout out of it. When they leave the pool and are cleared to run, they haven’t lost much at all. Their aerobic conditioning is still there, and only takes a few days to readapt to running on the track. Just a thought.