How much exercise is safe when recovering from an arm injury?

Depends: This is a problem that requires a face-to-face meeting with your doctor. In that meeting, your doctor will listen to you, perform a throrough examination and possibly order labs or other tests. Based on this information, he/she will be able to tell you what's wrong and what to do about it.

Hard to say: Since we don't know the type or extent of the injury, or whether it was as simple as a bruise or involved placement of metal plates and screws, no broad answer can be given. Sometimes if you provide detail we can offer more info, but this really requires a review by someone with access to your history & an exam.