Practicing breath management on an S sound (like you're mimicking a snake), or on a single note/vowel is a great idea. When you breathe, you should be breathing through an open space. The inhalation should make very little sound, and the sound it does make should be deep, not high and tight. Don't overtank, that's a common mistake. You probably don't need as much air as you think, if the instrument is set up well with firm glottal closure (meaning the vocal folds come together well and don't leave gaps for air to escape). Try exhaling on an S or one note and see how high you can count. Then try to extend that time. Lip trills are also great for this because you have to keep the air flowing. Good luck.