There are lots of things at play here.
First of all, starting and stopping any birth control can cause spotting and weird bleeding.
Second, some types of b/c just make your period really light or go away all together. There is nothing wrong with this.
Third, these other conditions you have (the cyst and sti) may have effects as well. I'm not sure.
When you are starting to have weird spotting and stuff, in general you should just keep taking your pill and stick it out. Giving your body a rest from the pill won't make you more regular, it will mess you up more. You might have to deal with the weird bleeding for a couple months from when you restart, even if that never happened the first time you started. When you're on any antibiotics, make sure you use a back up method for a while because they make the pill less effective.