My 2 cents is that:
You need to do something about your mindset.
1. You need to get rid of the habit of sight reading which is very prevalent of music students in my country:
2. You also need to get out of the mold and mindset where you must everything written for you. Let's just say that Jazz Musicians can hardly play the same piece exactly the same way twice with the same feel, same style or same notes.
Jazz is about 'Freedom' whereas a mainstream, classically trained student is used to playing exactly what's written.
A good start to jazzing is start with Melody Faking: using the repeated notes style, use the attentive style, use lots of syncopation and anticipation while retaining the melody motive, play around with lots of ornaments. A favourite folk song I like to "Little Brown Jug" and "Mack the Knife". Google Youtube to hear these songs.
And while doing that, developed the swing feel (where 2 quaver notes develop the long-short feeling - reminding you a bouncing ball). This one is best taught interactively with a coach where offline or online.
Once you catch the swing feel and developed your ability to melody fake, they you can move on to do ad-lib where you have total freedom to do whatever you want with music. Take your time. A mainstream note-reading student is going to find this a huge change of mindset.
Of course, one more aspect is your ability to play "by ear" so that you can deal with the harmony.
If you need any elaboration, you need to PM me.