Hello,
If you suffer from dysmenorrhea (painful menses) or irregular menses, yes, the
birth control pill can be used to help regulate your menstrual cycle and improve dysmenorrhea. In your case, having had a tubal ligation, the indication would not be for birth control but for the symptoms you describe and that is fine.
I'm not sure what you mean by taking four pills. You should take it as you otherwise would: one pill at the same time each day.