I ask because I noticed Emma and Kitty both got headaches when their powers first started manifesting and Kitty isn't a telepath so it can't be just telepaths who get headaches.

Lol, that's true... Most of the five lights had headaches too

I think a great deal of mutants do experience headache's in the wake of their manifestations. Almost all telepaths obviously because of obvious reasons. I cannot be 100% certain, but I do believe that Scott had head pains upon his manifestation. It's not all mutants, of those who've I've seen on panel's manifesting, Mercury, Stacy X, Dust, Rogue, they didn't express symptoms of head aches.

I never read any of Kitty's origins, or seen any flashbacks, so I'm not familiar with her manifestation.

I didn't know about Emma getting them, but I remembered both Kitty and Skin got them when they used their powers at first. It does make sense that characters with telepathy (or telekinesis) would get them, I imagine, but I don't think it's a general rule across the board.

...Nah.

I think they use that as an excuse to get out of having sex.....