Time of day might also be a factor, as I often get up early to take showers, and I guess if it's too hot, maybe it's too much at all once.

Still, reducing the heat has definitely been helping. It's weird, I just decided to look it up online ("Headaches after taking a shower") and boom, first site I found said it was because the water was probably too hot. And yeah, I usually take my showers in the morning, unless it's after my Friday night workout. Then I shower both in the morning and after that workout.