Dont worry about improving that specific recording. If I were you, I would find a karaoke version of the song on youtube, and then record vocals on it using your computer. Maybe add some reverb/delay to make it sound nice.
The recording you posted shows your talent, and I think that was your purpose. Now taking it further and start vocal training unless you have already, and put 110% of yourself into the music. Your young and you can reach the stars if you put the effort. :cool:
Good luck!!!