I chew sugar free gum like a beast. I'm sure if there was a glow in the dark meter of aspartame in one's body, you'd need sunglasses to look at me.
I started chewing the gum to curb the intense burning/pain of burning mouth syndrome that I have. I never drank large quantities of sugar free cola (drank the sugary stuff), though as it's been pointed out, aspartame, MSG, etc are in virtually everything these days.
mrsD, as you know I'm also a label reader.

It's great to be conscious of what we're ingesting.
With all said, I don't know if aspartame causes me headache. I think I just am prone to headaches (before the chewing gum, I was getting headaches regularly anyways, think it's safe to say I can't avoid them easily). I do know of 1 type of gum in particular that happens to be sugar free (aspartame) that eases the burning in my mouth, so I stick with what works - relieving the burning for me is more important than worrying about the aspartame!
I am also pro-eliminate something in your diet that's unnecessary to see if it works, so have at it with trying to avoid the aspartame and good luck! I'm on a current campaign to avoid trans fats entirely (and I can only go by the amount that's disclosed on labels - I'm aware below a certain % they don't need to mention it). I found food in the USA at grocery stores (which differs slightly in some cases, entirely in others from our food selection in Canada) had zero trans fats for the most part (at least the foods I was looking at). Canada doesn't seem to have cracked down as much on Trans (!). Some things I look at the label on, shake my head, "Why is it that this HAD to contain trans? Surely they could have avoided the Trans by removing something!".
Good luck again!