Great question! You've brought up a lot of different issues, so let's tackle them one at a time.
First, evaluating adverse effects from herbal supplements (i.e. non-medicines like tea) can be tricky. Just because something is "natural" doesn't mean it's safe. In fact, there are a number of nutritional supplements that can cause dangerous interactions with medications or medical conditions. It's often because there are lots of chemical compounds in these concoctions that can potentially have all sorts of effects. Also, each person, with their unique genetic signature, reacts differently. Furthermore, just like you noticed how different brands of green tea affect you differently, each individual product has different chemical properties. That is, each company has its own unique variation of plant species and manufacturing processing, which means that two brands with the same name on the label can have vastly different chemical compositions.
In terms of the medical evidence for or against green tea, it's weak at best. Very few reputable studies exist to say definitively whether it's "good for you" or causes harm. Some researchers say green tea slightly reduces the risk of lung cancer and prostate cancer, plus slightly increasing in bone density. Caffeine, however, slightly increases the risk of some cancers. All in all, the cancer risk seems to be a wash - there's no good evidence that coffee, tea, or other forms of caffeinated drinks affect the risk of cancer. There's some evidence that high doses of green tea extracts can cause liver damage, but such reactions are uncommon and usually reversible once the product is discontinued.
In your case, I suspect there's something in green tea that doesn't sit well with your specific biological makeup. It's not likely an allergy, but perhaps an intolerance? That term gets tossed around a lot (often misused), but many people simply don't react well to certain medications, herbals, or foods. I have a couple of patients who get headaches and diarrhea anytime they eat raw onions. Others don't like consuming gluten, even though they show no evidence of celiac disease on biopsy of their small intestine. Lots of people get nasty reactions from red wine and dark chocolate, while others think they're heavenly. I like how you have the insight to know that not everything you read on the internet is accurate. Despite blogs saying "green tea is super healthy", it's not actually healthy for you because it gives you a headache, jitters, and nausea every time you drink it.
So, I don't have a great reason for why green tea causes you problems, but it's safe to say continuing to avoid it is probably in your best interest
Hope that helps!