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If your mouth breathing isn't a structural or mouth issue, then it's a habit. Breaking the habit is a matter of correcting the behavior when you notice you're doing it. Breath through your nose instead of your mouth whenever you notice that you're doing it. If you're having issues breathing through your nose because it's a habit, you can leave written reminders for yourself. Write "breathing" on sticky notes and place them on your computer or inside of books to remind yourself to use your nose to breathe. If your nose is stuffed from allergies or a cold, over-the-counter nasal sprays may be able to clear your nostrils and help your breath through your nose. Purchase the spray from a drugstore and read the directions before using it. Clear your nose first by blowing it, then carefully place the end of the nozzle into your nostril and press down on the applicator to spray the solution into your nose. Sheets and carpets can harbor pet dander and dust and can make allergies worse. Cleaning them once a week will prevent dust buildup and can make it easier to breathe through your nose. If you sleep with your pet, you should try to sleep without them to see if that clears up your nose. Upholstered furniture is more likely to trap dirt and dust. Use leather, wooden, or vinyl furniture instead. Breathe through your nose for 2-3 minutes straight, then close your mouth, inhale deeply, and pinch your nose with your fingers. When you can't hold your breath any longer, slowly start to exhale through your nose. Continue to do this several times until you clear your nose. Many exercises like running, biking, and yoga require good breathing technique. If you get trained by a professional, they will give you the techniques you need to breathe properly through your nose. Look for classes locally and talk to your trainer about your mouth breathing problem.
Breathe through your nose when you notice you're using your mouth. Use sticky notes to remind yourself to breathe through your nose. Use a nasal spray to clear up obstructed nostrils. Clean your sheets and carpets once a week. Perform nose clearing exercises. Participate in yoga or other exercises that concentrate on breathing.