Teething issues with 4 mo old!

Alyssa
My 4 month old has started teething, and he always has his fingers in his mouth. This obviously isn't an issue, besides the fact that sometimes he sticks his fingers so far back in his mouth they reach his throat and it makes him gag and sometimes vomit up all of his milk!!!!! Has this happened to anyone else? I've resorted back to putting socks on his hands 😕