There's no point adding stress to your already stressed-out upper respiratory system, and that's what the change in air pressure will do. Flying with cold or flu congestion can temporarily damage your eardrums as a result of pressure changes during takeoff and landing. If you must fly, use a decongestant and carry a nasal spray with you to use just before takeoff and landing. Chewing gum and swallowing frequently can also help relieve pressure.
Mint has been used for hundreds of years as a health remedy. Peppermint oil might help with irritable bowel syndrome -- a long-term condition that can cause cramps, bloating, gas, diarrhea, and constipation -- and it may be good for headaches as well. More studies are needed to see how much it helps and why. People use the leaf for other conditions, too, but there’s very little evidence it helps with any of them.