Use two small vicegrips. Put one on the nosepiece and the other on the body of the handpiece. Turn vicegrips to the opposite direction, and it will be easy to separate. Soak everything in WD40 and blow dry with compressed air. Use essential oil to lubricate, and everything will be fine.
I'm not going to put anything on it. That could lead to even bigger losses. You need to call your dentist and make an appointment to see them. Just don't bite on your front teeth (at least for now!). Good luck with your teeth!
Later added: I won't go to the pharmacy to buy a temporary material. In most cases, the dentist will take the material out of your hand when you don't need it, and if you don't need it, you can take it out.
