It seems like if you just sing all the time it will get better, but will vocal lessons really make you get better faster?
It depends on how good your teacher is. I took vocal lessons for a year when I was 11, and my teacher was horrible. My singing actually got *worse*, and I began to pick up bad singing habbits. (i.e.: singing more through the nose). I quit, and just began singing on my own, for school plays and such, and got much better practicing by myself and tape recording my voice, to listen to again.
However, I did start vocal lessons three months ago, again, and I have an amazing teacher, who actually works with me on improving my range and such.
So, if I were you, just ask around and see where you can take good lessons with experienced teachers, and go for it!