If I do get it looked at and they say I nicked the nerve, does it heal on it's own?
Yes, nerves generally heal very well on their own. Just like when you cut your finger. It hurts as nerves are being severed, but they still grow back, which is why we do no lose feeling after the wound heals.
If you have your ozone unit place a bag over your hand and place the output tube in to the bag and seal it off loosely with some tape then blow the ozone in the bag for a half an hour or so. Repeat this a few times a day. That will help with any infection and speed the healing process.