On my 3rd month of birth control and seemingly randomly suffering PMS symptoms (sensitive breasts, moodiness, etc.), duration 5 days. Why/how to fix?

Birth control. My first concern would be that of the "right birth control pill". Check with your doctor and ask if there is another bcp that may be more helpful since the currrent one is not working as you expected. It might take a few weeks to get used to it.However, still talk about other options and breast pain and moodiness. Also, a mood stabilizer might be helpful such as an antidepressant.