Unfortunately, I've had 2, but mine were not the same as yours.
My first horse had hay fever. He was allergic to a certain pollen that came out during spring/summer. The first year I had him, we rode past the offending tree - and it was like he was stung. He head shook for about a month very lightly. The following year I moved agistment, and in summer he was in full swing of head tossing. The poor guy was so frustrated. I used a jab on him to help him, which resolved the issue, and sold him on to a home further south where this pollen was not commonly found. He hasn't shook since.
My second horse with this was a facial nerve - she had a tooth extracted, and started to head toss. Unfortunately it took 2 weeks, various jabs (anti-histamines, steriods, etc) with no luck. By chance, I had a bowen course coming up (I am training in bowen and sports massage), and took her along in my last hopes of trying to get her sorted. She did a full session with her, and by the end of it - she wasn't head shaking. And she hasn't since.
There are several types of head tossing/shaking - light sensitivity, open pores, allergies, trapped or tweaked nerves, dental issues, poll issues, sinus issues ..
There are ways to help them :)