Are you sure that you're holding your fingers over all the holes when going up there, and that you're keeping your tongue high enough in the mouth? (think "EE" for about where it is!) Having a separate fingering shouldn't be much of a problem-if it is, then keep your right hand down on the keys for open G up to Bb, and work on keeping your fingers still close to the rest of the keys when hitting stuff like the register key.
Are you taking lessons? A good teacher in person could help you a lot better than someone trying to guess what's going on over the internet!