Listen to great blues players. NOT necessarily sax players, but singers, guitarists, keys, bass, horns...all who are immersed in this genera. Yes, they play notes, and yes it's usually notes that fit within the chord structure. However what makes those blues masters special is that they communicate beyond those notes and touch people's emotions. It's up to you if you wish to go there. Most jazz players are content to just play quickly and try to impress with their technical prowess. A few are successful, but they almost always have something more than technical chops to offer.
It's never too early to put yourself into the music you play. In the blues, if there is no existing/particular song/lyrics, then you are the storyteller. The song/story is up to you. You're doing the playing. It's the same for a singer. You're either telling your own story or somebody else's. In either case your job is to communicate something more than words or notes. A computer can play notes absolutely perfectly and precisely but who wants to listen? It's about human emotions, feelings. It's the difference between paint by the numbers and an art work. The difference between hearing somebody read a script and having a great actor who makes you feel the emotions of the moment. Enough said?