There are two parts to becoming a career musician; music theory/knowledge and having a good ear. Both parts are equally important and both parts need to be developed in order to become a well rounded musician. Having one without the other will just leave you unbalanced and unprepared. Music theory prepares you to read music and know why it is you do what you do on your instrument. Training your ear allows you to quickly recognize parts, progressions, and overall feel for the music you are playing.
Is it possible to have a great ear, yet know nothing about music theory or reading music and still make a living as a musician? Or is it possible to know a lot about music theory and reading but have a bad ear and still make a living? I would say "yes" to both questions, but you will be limited to what gigs you can play or what jobs you can take. For example: if you can't read music, it will eliminate most jazz, classical, composition, teaching, and pro studio gigs. By developing both parts of your musicianship it will open the doors to many more opportunities.
If you build your knowledge of music/theory you will not only learn to read music but you will learn why you do what you do on your instrument. This in turn opens up the floodgates for creativity. If you want to develop your knowledge of music and theory, take private lessons, take music theory classes at your local college, and read books about it.
By developing a good ear you will be quick to recognize parts and progressions on your instrument. You will also build a great feel for music. I often tell my students that "I can teach you to play funk, but I can't teach you to be funky." This comes from having a great ear and feel for funk music. To develop your ear listen to the genre of music you are trying to play (tons of it!), take ear training classes from your local college, transcribe parts, and take private lessons.
There is no "get rich quick" formula to becoming a career musician. It is the results of years practicing, studying, listening, and learning both music theory and training your ear. Be encouraged to get out there and start training both parts of your musicianship.
Zach Meade has been teaching drum lessons for 15 years. He received his B.A. in Music performance in 2005. He has had 2 of his blogs published on the blackpage.net (an online drum magazine)