Is my metabolism permanently broken or damaged?

No. No matter how you have restricted, in what ways you have restricted, for how long or how severely you have restricted, how many times you have reactively eaten, purged, abused laxatives, diuretics, compulsively exercised through injuries and exhaustion...your metabolism will return to normal if you pursue complete weight restoration.

Obviously if there are complex additional medical problems involved, then it will be for your physician to make the final determination on your metabolic state, but restrictive behaviors in and of themselves do not break metabolic function.

You need to eat no less than minimum guidelines every day to provide enough energy for weight restoration, physical repair, (maturation as applicable -- if under age 25) and then the metabolism returns to its optimal state.

Metabolic rate drops to keep you alive when you are not bringing in enough energy to support all the biological functions in your body. In fact, your metabolism is the opposite of broken -- it is doing exactly what it needs to do to keep you alive over the short term. If you restore the energy balance in your body, your metabolism restores to its optimal state along with that process.