If you leave a wound, it will fester. Ultimately. And should that be allowed to happen, it could get worse, a lot worse than you could ever have imagined. So imagine having to lose at least a part of your limbs as a result of your ignorance or lack of care. Life is challenging now; it could be a lot more so if you act this way. Or not. So then, when a hand injury, knee injury, foot injury, head injury, whatever the injurious case may be, treat it immediately.
It is in your best interests if you do so.
Any injury is not to be trifled with. What this means is that you should not be taking the law into your own hands if you will. And how often does that happen, much to the detriment of some of those who dare to try. They are faced with the prospect of a lifelong battle against the injury. Perfect use of the hand cannot be restored. But without passing aspersions and should that be the case then at least partial use of the hand can be restored.
If no restoration is possible, then there is always rehabilitation in the sense that the patient is being given every physical and mental encouragement to make the most of a bad situation if you will. All is not lost. The patient is, however, faced with a lifelong journey of physical therapy. Let the general physician diagnose the injury as early as possible. If it does appear acute or severe, she will be making referrals.
And so let the specialist physician treat the injury and help the patient restore the full use of his hands. So when it happens, treat the injury immediately.