You're on the right track. Every time you get a tight band around your head, it's a tension headache. Every time you feel your head squeezed, it's a tension headache. Whenever make sudden changes to the way you eat, like cutting out soda or upping your potassium, you'll get a headache as a side effect of your body adjusting to the change. Every time you worry about having a tension headache, you'll get more tension headaches. Anxiety coupled with tension headaches does affect your concentration, impairs your ability to think sharply, and gives you a bit of a foggy head.
Assuming that your doctor when you see them agrees it's just tension headaches too, you might want to try to find some ways to ease the tension. Head, neck and shoulder stretches help if you do them, eating more magnesium like pumpkin seeds helps. Whenever you feel that tight band around your head again, you need to stop that "what if it's X" or "what's if it's Y" loop before it starts. You know the answer but may you still doubt that 'tension headache' is good enough or acceptable as an answer.. because the terrible sensations you feel seem to outweigh something as benign and harmless as a tension headache (comparative to say cancer. I know tension headaches aren't fun so I don't want to devalue their discomfort either).
Remember that anxiety exaggerates what's really going on. You're actually in a pattern now where you're kind of rewarding yourself every time you worry because when your 'fear' doesn't actually pan out, you get relief and are glad that you worried - as if worrying actually prevented your fear. As if worrying has some magical power to stop things from happening. That's a false belief.