I can't really think of a reason those specific drinks would give you a headache.

I compared the ingredients of coke cherry zero with regular coke zero, and the ingredient lists are almost literally identical. The only difference would be in the flavoring they use, both of which are just listed as "Natural Flavors".

The only other difference is coke cherry zero has marginally more Acesulfate Potasium or less Potassium Citrate. We can tell because their position on the ingredient list is swapped. It's not well known, but ingredient lists are sorted from highest to lowest content.

Potasium Citrate is found in many foods, in particular in lemons, grapefruit and pomegranates. It's added for preservation and flavor.

Acesulfate Potasium is another artificial sweetener, with sweetness on par with Aspartame. Like aspartame, it's a very well studied food additive and is deemed completely safe by regulators.

But again, both drinks contain them, so even if we disregard that they are safe, the small difference in content is very very unlikely to cause any effect.

And you don't have to be an idiot to be susceptible to confirmation bias. Our brains are built to look for patterns, but sometimes they see them where they don't exist.

As for #2, really any amount of sugary drinks is bad for you. This includes fruit juices (including "no sugar added" and freshly pressed). The problem comes from how fast your body absorbs the sugar. Sugar dissolved in water is very quickly absorbed and causes a rapid spike in blood glucose. These spikes put you at risk of developing a range of nasty conditions - in particular Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease. Of course drinking one can won't immidiately give you those conditions, not unlike how smoking one cigarette won't immidiately give you lung cancer. But like there is no "healthy" number of cigarettes you can smoke, there is no healthy amount of sugary drinks you can consume.

It's best to avoid, but of course nobody is expected to live perfectly healthy lives, so drinking a can now and then will probably not harm you.

If you want to have a sugary drink, make sure you do not drink it on an empty stomach. Drinking it with a meal will slow down how quickly sugar is absorbed. For the same reason, eating sweet fruits like apples is perfectly healthy despite relatively high sugar content. The sugar is locked inside the solids of the fruit and is absorbed slowly.

Artificial sweeteners are usually 200-1000 times sweeter than sugar, so their content is tiny compared to sugar. A can of coke zero contains 87mg of aspartame. Aspartame has no effect on blood glucose or insulin levels. Even if it did, such a tiny amount could not cause a spike.

This is why I get agitated with headlines like these. WHO announces some study that they haven't even published that says aspartame "might be carcinogenic" which flies in the face of decades of research and widespread usage. And thousands of fear mongering articles will push the already misinformed public to drinking sugary drinks that in contrast are practically poison.