A broken wing usually hangs lower than normal so if one is trailing on the floor then it is more than likely broken also if you watch the bird try to fly if a wing doesn't fully extend when it flaps then this is another sign, breaks can usually be felt when a wing is extended, a healthy bird will be able to pull the wing back sharply when you release it, if it is broken it will more than likely hang limply, depending on the type of break pure cage rest may be all that is needed, I wouldn't recommend keeping it as a pet especially if you can make it better, it's a wild bird and will not be happy permanently caged, if the wing is broken and doesn't heal then keeping it as a pet may be an option or putting it down but the decision is ultimately yours.