Re: How to become a intermediate-professional saxophonist
Continue to challenge yourself. Practice for the love of playing and for the desire to get better. Set goals and work hard to achieve them. Don't get caught up in the game of needing awards or competitions to feel good about your playing.
My suggestion would be to find a few of the top level professionals in your area and ask them if they would be willing to teach a highly motivated student who loves the saxophone. Even if its just a couple lessons, a good professional can throw a lot of stuff at you that will keep you busy for a long time.
Its difficult to give advise on what you should practice without knowing what you've been working on and where you are in your development on the instrument. One recommendation if you don't already have it is the 1963 Larry Teal book, "The Art of Saxophone Playing". Although saxophone pedagogy has progressed since this book was written, there's nothing in it that's out of date. Taking the time to give serious study to this book will certainly be a boost towards getting to the next level.