★★★★★
There are estimates that many "sinus headaches" are actually migraines. This was the case with me. I had years of sinus infections, but after my migraines began and I started treating them (with prescription triptan class migraine meds), I began paying more attention to possible migraine triggers and realized that the "sinus headaches" I got whenever A/C was blowing on my head/face were actually migraines. I had only slight improvement when trying methods to help sinus congestion/irritation, but these headaches did respond very well to migraine meds.
I still have sinus issues and agree that A/C will irritate sinuses by drying them out, so repeated exposure to A/C blowing on you would most likely lead to sinus problems, but if you get a "sinus headache" directly after A/C is blowing on you, then you may want to look into a migraine treatment.
I was skeptical at first because they really feel like sinus headaches to me, but the response to migraine meds (not sinus treatments) for these specific headaches convinced me that they were migraines instead.