Promise not to laugh at the reason, but I have trouble sleeping when I'm having my period too. I'm older, and my flow is so light that I haven't used tampons in years. BUT, I also have slept in the nude for years, and during my period I have to wear underwear with the lightday pads. I am driven Nuts having something binding me around the legs and hence, there I am with Insomnia!!
Surprisingly enough, it took me a while to connect the two and thought I'd share just on the off-chance that it might apply to you...