Baby won't stop gagging herself

Na

Gah! Is there anything I can do to stop my teething 4 month old from constantly shoving her hands in her mouth and gagging herself?! I'm sure there's probably not but I had to ask. 😣

It wouldn't bother me so much but she makes herself spit up multiple times a day.

Should I just keep a bib on her and call it a day? 🙄