Professor gave me a higher grade than I deserved. What should I do?
Don't worry about it. No one's going to come after you for failing to turn in an essay in some random course. No one's ever going to check and, if they did, they probably won't care too much. 

Should you turn yourself in? No. There's absolutely no reason to turn yourself in. You've done nothing wrong. The professor is the one responsible for assigning your grade correctly. For all you (or we) know, they felt you deserved a B-.

Should you have emailed your professor the essay? Probably not, but mostly because they probably don't care. I doubt they read it and I very much doubt that you caused any problems for them.