Putting up with headaches every day really interferes with living a normally comfortable life, but people with migraines often get more sympathy. Chronic daily headaches are not usually associated with allergy except where sinus problems result from inhalant allergens. But, as you have found, they can be associated with foods as well. The good news is that allergy tests are the beginning of the phase of diet investigation. They show the body is reactive, but not that all the foods need to be excluded forever. Over time you can test those that you want to try using the new thinking. This is to start with very, very, small amounts of your favourite food and increase over days to desensitise yourself, and then keep a very small amount of that food in your diet every day once you tolerate it.
But there seems to be another part to your story, and that is that even if you try to exclude all the foods that were positive on the allergy list you still feel you are reacting. It is no wonder you can feel lost. This part says that it might be wise to add on another way to investigate diet. This is to do what the patients in my research have found useful. That is to use the Diet Detective approach to investigate your headaches. Do read the article on the Family Sensitivity History as that gives you clues which are as important as allergy tests https://foodintolerancepro.com/category/food-intolerance/the-family-sensitivity-history/
Then you can obtain Are You Food Sensitive? from this website and use it to guide you through the process. This approach covers chemicals in additives and foods that most often cause headaches in food sensitive people.
Keep your allergy tests handy and exclude any you really feel do cause headaches, otherwise follow the diet detective process, and after four weeks you have a baseline to test various food from. Those test foods can be any of your favourite foods. My book Tolerating Troublesome Foods gives hints on over 300 foods showing how to test them so you have the best chance of tolerance. The process is tricky but worth the effort. The other tricky part is that often foods you think may help, such as tea or mints, are foods that actually produce headaches 24 hours later, so it is no wonder you didn’t suspect them before. I also suspect the allergy tests did not suggest attending to smells in your environment. That is also explained in Are You Food Sensitive?
I feel for you. It is so frustrating that the medical community do not understand food sensitivity. We do not know what the mechanism is but if you look at the articles on my site you will see that it is more likely to be slower metabolism of these food chemicals such that the increased amounts of the metabolites, [some call them toxins], interfere with body functions and cause symptoms. This is because each person has their own symptoms and end up on their own diet after testing many suspect foods. You can do what others do: use my books and when you find them useful tell your doctor so he or she understands what is happening for you.