Depends on the type of fracture. Hands generally heal faster than other parts of the body though.
It was nonsurgical, so it will probably be a couple weeks or more. There are lots of nerve endings in your hand, so pain will be expected. Ice can help. Even holding a really cold beer can can help.
I’ve broken multiple fingers, and they don’t all line up anymore. But they still function as they used to, once healed.
The finger may ache for some time. When a bone breaks, your body creates a ball of bone around the fracture. Then, it will widdle it down to appropriate shape, and fill in the empty spaces. Then. Almost as good as new!
It probably wouldn’t hurt to pursue foods high in calcium, while it heals, or take a supplement, or tums (as directed.)
Holding the hand above/higher than your heart, when possible, will help with pain and swelling, as the blood won’t pool there. So. If you’re sleeping, try to elevate it on a pillow, or bed frame.
The worst part of a broken finger, is that you’ll learn exactly how much you actually use each finger. And you’ll probably accidentally hurt it repeatedly. Icing it down before bedtime, will keep it numb enough to fall asleep. Anri-inflammatory drugs, like naproxen/Alieve, can help. If you are using something with acetomenophen (like Tylenol,) make sure to limit or reduce your alcohol consumption. Such drugs are tough on your liver.
Keeping a piece of tape around the finger can remind you to be careful with it. It’ll stop hurting constantly soon. But you can reignite the pain by hitting it on something accidentally.
Good luck.
Peace n love.