How are you hitting the draw? If it is by aiming to the right of the target and turning the club face towards the target, then it may be that your club face at impact is too closed.
When I first started playing I was a slicer, never really had a problem with hooks. But when practice, sometimes I fool around deliberately trying to hit hooks and it is quite easy to do by swinging in-to-out, but what makes a more drastic effect is turning the hands over, so this could be your problem. Difficult to know without seeing.