Yep, the tooth needs attention. As for the cut, about a year ago I took a bad fall (face first) and my tooth nearly tore through my upper lip. I had a huge gash, very deep and about and inch long. I went to the ER because of that, and the doc said it will heal itself. They would have stitched it only if it went through my skin.

I hope you heal up fast, and wear a helmet from now on. Consider yourself lucky. It saved my life when I went down.