Okay, first off, Headache medicine may not be as competitive as other subspecialites, but there are some competitive programs out there within the field.
Jefferson has more than enough applicants to choose from
Most of the programs within NYC interview and apply very early. I believe it was St. Lukes/Roosevelt that decides by March who their chosen fellow is?
Mayo has two programs, one in Rochester and one in Scottsdale. Its Mayo, they fill and their internal application is fairly competitive. Some program that I applied to pretty much wanted LOR and to see your CV. Mayo asked for my genetic karyotype (that was a joke, not being serious, but they did probe hard).
All of the NYC programs fill fast and early!!! (see my comment above). Lipton is at Albert Einstein and is considered one of those giants that walks on water, thus, they all fill fast.
At the end of the day, headache medicine is like every other specialty, the top/competitive programs fill fast and early and yes, would require a solid CV and perhaps some research. The other programs, well, it will not hurt you.
But you're a PGY-3? Nothing fancy needs to be done here to show your interest. Case report? A simple idea that will publish a poster at the next scientific meeting (if you see the crap they accept, you'd realize this is not hard to do).
But indeed, it probably is a little to late in your residency to obtain IRB approval for a big study.