Barbara, you can register copyright on the music; The teacher you refer to can register copyright on the arrangement. If anyone uses the music in a different arrangement, they owe royalties to you, but not to the teacher. If they use the teacher's arrangement of your music, they would owe both of you. Collecting the royalties is another matter. Unless you are able to find out on your own that someone used it, you probably won't get paid. Unfortunately, that's what BMI and ASCAP are for, and they take half. As far as marketing your music, as in showing it around to people that might want to use it, you could do that yourself if you have the time, but it's more common to contract with a publishing company to do that for you, but they also take a share. There's generally not a lot of money in writing music, unless somebody has a hit with your stuff. When Elvis was alive, every pro songwriter's dream was to have him record one of their songs, because that would automatically mean a lot of money from album sales, even if their song were not the hit song on the album.

Good luck, Chet