When you play jazz, you're expected to be able to solo. When you have been trained as a classical musician, to read notes accurately, it's hard to trust to get free of the notes, a bit like swimming without water wings.
Arnie Lawrence once told me an anecdote about Dizzy Gillespie. A radio interviewer once commented that, since Dizzy and his fellow musicians played without written notes, they must make a lot of mistakes. Dizzy just laughed.
On the one hand, it's true that if you play a song by ear, without the notes before your eyes, you're liable to make mistakes. That's why big bands, jazz orchestras, have written parts. But in jazz, it doesn't exactly matter whether you play the right notes, the way it matters whether a pianist performing a Beethoven concerto with a symphony orchestra had better play exactly what Beethoven wrote. The classical performer's interpretive freedom thrives on what Beethoven didn't write. The jazz performer's interpretive freedom is much greater, not that every jazz musician who takes a solo is as profound and creative as Beethoven (to state the obvious).
Fortunately for me, in the past couple of years I've been playing in an amateur big band, where the director encourages us to solo, even if we're not very good at it. This, by the way, is in contrast to the big band that I played in for about ten years, whose director only gave solos to the musicians in the band who were best at it, so the rest of us never had practice in soloing.
I've been getting more confident in taking solos and enjoying the risk and creativity. I heard Sonny Rollins say in an interview that when he soloed in performances, he never knew exactly what he would play. Arnie Lawrence said that when you solo you have to play what God tells you to play. I'm lightyears behind Sonny and Arnie in musical ability, but I take inspiration from them. You have to play what comes to you on the spot.
When I solo, I don't have the chord progressions firmly in my ears. I have to look at the chord symbols to guide me and keep me in the right place. But I'm getting better at hearing the changes and listening to what the band's rhythm section is playing. I'm also getting better at hearing what other soloists do, both my fellow musicians in the band, and the great professionals I hear in recordings.
