There are things that they can get that cause wing or leg immobility that are not trauma-related. We're talking bacterial infections that can cause arthritis-like conditions. In such cases (when you can't find evidence of a real injury), you can try a course of antibiotics. Frankly, Doxycycline works the best for me anymore although I once had one that I'd begun treating with that but I had to go away for a few days so I took that bird to the vet for an injectable Penicillin that would last a few days. When I got back from the trip, the bird's lame leg seemed fine and has been ever since (many months).
That is to say that I don't see some of the telltale evidence from your picture that anything's broken. Usually, those have a few different ways that they present.
Pidgey