Yes, they will find out. There is a national database. Don’t attempt to hide this information. You need to be proactive. I’m assuming at this point t you’ve already invested considerable money and you clearly want to pursue a career as a dentist.
You say they don’t care. How do you know? Have you exhausted all avenues of appealing the dismissal? Have you had any discussions with the dean’s office to see if there are any ways to salvage your two years of dental school? If you’ve done all you can at your dental school, then yes, I think it’s worth consulting an educational lawyer too.