To "be recovered" means that your injury or sickness has healed.

The word "recovered" can refer to either the body part:

Is your shoulder recovered?

Or it can refer to the person:

I'm glad to see that you're recovered.

You could also say:

The question is whether his leg has fully recovered.

In fact, "has recovered" is probably more common than "is recovered":

Has your shoulder recovered?

I'm glad to see that you've recovered.