I grind my teeth when I'm under a lot of pressure. Is this a sign of a mental illness?

Probably not. Teeth grinding, also called bruxism, is a fairly common sign of tension, and it can cause problems with one's teeth. However, by itself, it is not suggestive of a mental illness, just that you are reaching your threshold of how much pressure you can handle. It's your body's signal for being overwhelmed.
Save $$$. See your dentist as soon as possible. Bruxism can destroy your teeth and then it will be very expensive. My advice is "asap".
Your dentist. Get a plastic bridge. Bruxism is bad for your teeth and your credit card.
Grind teeth. No, but it may be a sign of too much stress. See your doctor for help.
Other reasons. Along with stress, sleep apnea can cause grinding. And then there are others who grind for an unknown reason.
Sleep problem? Bruxism is sometimes related to sleep disorders. A sleep study may be useful.