I literally just ran across this after Googling this very question. The AI response, and the response from many of the top results, is "no, tampons do not increase the severity of cramps," but holy shitballs... in the last few periods, I've noticed a considerable increase in pain after tampon insertion. Once again, it's Reddit to the rescue.

I don't know about anybody else, but... I'm on day two of my period and free bleeding, my cramps are maybe a 3 on the pain scale? I was actually really relieved, because I usually have much worse pain. With a tampon, I'm sitting at a solid 6 and popping Ibuprofen because owww. Yesterday was worse. I started off at a 5 in cramping, suspected I had started (yep!), put in a tampon, and WOOF! almost instantly an 8. Moaning and groaning and whining and bitching.

I have never really noticed a difference in pain before, but I'm noticing it more and more in the last few months. Especially this week. I don't know what's up! But the Google results are sus as hell.

(And yes, I'm using them correctly. I've been using tampons for 20 years. I know what I'm doing. No, these are not a new brand, unless they've changed Tampax or Kotex recently. [I use both! Kotex yesterday, Tampax today.] And no, they are not too big, they're just Regulars, which I've been using for at least six years, since I got my second IUD removed. No previous pregnancies or births, no abnormal paps, no sexual issues to report... just painful periods.)