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If you're trying to study or work, bring your laptop or books with you to a public place. Many people go to libraries, cafes, and parks when they need to focus. If you have a car, simply driving to a parking lot or a garage can be the escape you need. If you're avoiding your sibling for other reasons, try going for walks or hanging out with friends more often. Try your best to make yourself busy outside of your home. If you have your own bedroom, locking the door is the best way to ensure your privacy, if you're allowed to. This will cut down on any unwanted intrusions into your space. This is especially important if your sibling has a bad habit of not knocking or is too young to realize that it's the polite thing to do. This is your best option if you share a room or will be with your sibling on a long car ride. If you use headphones, just be careful not to raise the volume too loud or you may damage your ears. Active noise-cancelling headphones can block out noise without the need for high volumes. Deep breathing exercises work to relax you and may be a great help if you find yourself getting angry or annoyed at your sibling. Inhale slowly through your nose while mentally counting to five. Exhale slowly through your nose. Repeat this until you're calm enough that your sibling no longer bothers you.
Get out of the house more. Lock your bedroom door. Wear headphones or earplugs. Reduce stress through deep breathing exercises.