I think everyone’s kid goes through this stage! Kids love to find something they can be in control over - and often by exploring their own mouth they work out they can make themselves gag, how exciting!! Depending on how we react in the moment, your child can also control the room. “Wow - when I stick my fingers down my throat, I make a funny noise AND my dad shouts “stop it, you’ll be sick!””. Remember - any attention is good attention, so if you don’t want your child to repetitively make themselves gag and vomit, try to respond calmly and appear almost bored. Move their hand and try to replace it with a new behaviour. Clap their hands together or bang on something.
My son always chose to do this in the car and it would scare the life out of me! He definitely vomited a few times. I hope this saves someone a load of washing!