Yes, just about every time I would miss a few days of Synthroid when I'd forget to get a refill or whatever, my period would be late. Once I missed like a couple weeks of it, and went 2 months without a period. But it's a bad idea to quit taking it altogether because it does throw your body off to not get the hormone it needs. If it is giving you headaches, either try a lower dose or a different brand and see if that helps.
Hypothyroid does cause menstrual irregularities and not taking your meds can mess you up pretty good. I stopped taking mine for 3 weeks on my doctors advise and I'm paying for it pretty bad now and trying to get re-adjusted. If your meds are causing headaches you should consult your doc and have them check your blood work to see if you are on too much but i wouldn't take myself off, it can be dangerous and make you sick...
My endo started me on 50 and I'm gradually working myself up to a stronger dose. Starting at too high might cause these symptoms. Some people have to start at 25.
Or maybe the synthetic drug isn't right for you. Other people do well on the natural drugs like Nature Thyroid or those made at a compounding pharmacy.
:) Tamra