John Connally heard the first shot. Therefore, he couldn't have been hit by that first shot.
Everything he said he did after hearing the first shot is captured on the Zapruder film. He had just turned his head from right to left, then he suddenly jerked his head back to his right, and there his head remained in that position until he appeared from behind the Stemmons Freeway sign, the sudden two-time up and down motion of his shoulders, and the grimace on his face are the first signs of him being struck by the shot that he did not hear, and then he heard the third shot which stuck President Kennedy in the head.
This can all be heard in the 1964 CBS program "The Warren Report", which aired the day the Warren Report was released to the public. Governor Connally gives a detailed account of what happened as soon as the car turned onto Elm Street.