I recently bruised the brachial nerve in my left arm, resulting in a total inability to exercise (and even breathe easily, due to sympathetic impulses in my ribcage/torso). I've been able to breathe deeply for about 2 days now, so I can do sprints and walk comfortably.

I don't want to do upper body work until this is completely healed. Would unweighted squats be sufficient, or do I need more?

I'm still losing weight, for what it's worth... even without the exercise.