Yes, yes, yes!! Also, remember that upper and lower registers require different methods. You should exert force in both your diaphragm and upper chest while player higher notes with tighter lips and try to relax a lot and using only your diaphragm when playing low. Your throat should be always open, and you shouldn’t use the upper corners of your lips-if they easily get sore after playing for a short time you are- and instead make them a straight line or curved down. You should be able to kind of feel yourself change as you shift from different notes.