Myself and two of my kids have this problem. My son and I gave up sulfate shampoo a year and a half ago and it solved the problem immediately. (my other child is not concerned about the issue and is an adult out on her own.) The issue did return for me several months ago and I was so disheartened until I discovered there was a sulfate in the cleanser I was using! I had read that label over and over and missed it every time! I immediately stopped using that cleanser and the problem resolved again. It was then I knew for me (and probably my kids) it's a reaction of some sort to sulfates.
You said you wash your hair once a week but only use shampoo/conditioner on the ends so I am not sure the sulfate things applies to you. But, you might want to try a BS/ACV routine - even just once a week may help. Make sure you also scrub your scalp well with your fingertips and rinse thoroughly.