He is a fixed point in time which should not be possible for a human, so the tardis tried to get rid of him
Not "get rid of", "get away from".
the Doctor felt guilty from leaving Jack on the GameStation and attempted to get away from him in a cowardly act. You can see this by the Doctor's face when he sees Jack
Yes. And, as the Doctor told Jack, both he and the TARDIS find Jack's proximity uncomfortable.