Speaking of weird periods...

I took a birth control pill starting in July 2014 and stopping after a few months because it caused me to go from having a 37-38 day cycle to getting my period (or at least bleeding pretty heavily) every other week (the main reason I was on the pill was to make my period stop). I took the same pill again briefly at the beginning of this year, then stopped again.
After that, my cycle was averaging about 28 days. Recently, however, my period has been showing up every other week, and I've been breaking out pretty badly. What could this mean?
(My SO and I had unprotected sex about a week and a half before this started in mid- to late August.)