Not necessarily.... Tee height can possibly have an affect on your ball flight, not just height, but also side spin. I don't want to get too technical because I am not a teacher, but.... If you make the same swing with the ball teed at different heights, you will get different impact positions for the head which can impart some additional side spin. Based on what you said, that your shots start straight and then curve to the right, it sounds more like you have a problem with an open face at impact. There are two types of slices, one where the ball starts left and makes a big banana to the right (caused more by an out to in swing path) or the ball that starts on a straight line and then curves right (caused by decent swing path but leaving the face open at impact). The latter seems to be your problem. I would practice making my normal swing but imagining trying to hit the ball with the toe of the club. This should get you turning your wrists and forearms over at impact and square your clubface, ridding you of the dreaded slice. Try it at slower swing speeds until you get a feel for it and gradually increase tempo until you are at your normal speed.