You should request a different cannula from your oxygen supplier. Ask for one described as, “extra-soft with a curved tip”. That should work much better. You might also ask the same supplier if they can provide a
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What you describe is called a “trans-tracheal oxygen system”. There is a lot of experience with this mode of oxygen delivery but it is usually used by people who require high-flow oxygen. And, it is not without complications, such as pain, bleeding, displacement, mucus plug formation or infection but these are usually mild or easily treatable. I suspect you would change your opinion of the nasal cannula if you were to try it, without complications, and give yourself time to get used to it. The nasal cannula has become a frequent sight in public in recent years.
Good luck.