I was in the "slowing going nearsighted and avoiding glasses" phase for quite some time and the result was regular "ice-pick" headaches and migraines. Getting glasses fully cured all of that. My prescription also hasn't changed in 10 years, so (for me, at least) glasses have only had a beneficial effect.
I've been nearsighted my entire life and do not wear glasses. I get the headaches after a couple of hours of wearing them. More than likely it's more to do with what you're accustomed with than how good your vision is.
It's fluctuated from -4.5 to -2.5 over the years. Currently on the better end I think, but I haven't been to an exam in a long while. I have friends with lower than -5 and from trying on their glasses, I would also wear them if my vision was that bad. Even at -4.5 the only major annoyances were street signs and confusing people from far away though.
That's insane to me, I'm at around -3.5 and I feel highly handicapped when I don't wear glasses. I most definitely wouldn't drive without them for instance.