I'd get my butt to the nearest emergency ward and have it checked out. Go by yourself or call an ambulance. Could be serious. There can be a lot of things that it means, but the biggest concern I would have is an allergic reaction. A severe allergic reaction to something can cause your throat feel tighter, difficulty breathing, and it might feel like someone is sitting on you. The person might also feel itchy, see a rash, or swelling elsewhere. This would be a severe reaction, though, and need immediate remedy because the throat is actually swelling in that event.
It can also mean a heart attack, though usually the person wouldn't notice a tightening of the throat through the pain in their chest or jaw.
It might also be an anxiety attack. Like I said, a lot of possibilities, but my concern