Ehhhhh I don't know if it is doctor worthy. I have a pinky toe that grows in split naturally, and anytime I stub it on something the outer half cracks off..I just make sure to keep antibiotic cream and bandaids handy while I wait for the piece to fall off and grow back. There is not much the doctor can do but tell you to keep it sterile.
I stuck a steak knife through my finger one night and went to the ER..The doc said save my money and just keep it sterile and put ointment on it..Love the country docs LOL.
Make sure it has time to breath every now and then. Fresh air is great to help the healing process. Now if it starts turning purple or pussing..that may be a problem