gag reflex?

i’ve been having tonsil stones a bit for the past year or so, kind of recurring for a few weeks here and there after I get sick, eat certain foods, etc.
And lately i’m having a hard time flushing it out because my gag reflex is literally crazy!!!!! like all the time!
I’m not sure if it’s a tonsil thing but my GP has mentioned that my tonsils are larger than usual. Like is it possible that they’re so huge & stuff is just getting stuck back there causing me to gag and feel nauseous all the time - it’s even bad when I brush my teeth!

also: do people get their tonsils removed for tonsil stones? does it help?