If you have regular headaches, see a doctor. Could be hay fever or other allergies for example and there's stuff that works much better for that than painkillers.
Yeah even OTC drugs aren't necessarily safe to take daily and indefinitely. Depending on the medication, you can end up with things like stomach ulcers or even liver damage. Once in a while is fine, but if you're needing to take something daily, you might want to get checked out and/or try some sort of other methods.
Usually it's tension headaches. The solution to that isn't meds, either, but chilling the fuck out and better posture. Yoga, callisthenics, actually pretty much any kind of sport should help. In acute cases, try a hot bath. Or some good Indica wait no that'd be meds. Valerian is probably as far as you should go, it's not a downer as such but makes it harder to forget that chilling out is an option, needs a regular schedule though if you're wired up. Eat healthy. Avoid hangovers by not getting drunk. Make sure your sleep quality is good. You know, basic shit.