My pdoc's and OB/GYN's have always warned about changing one or the other, psych meds or bc pills/hormones, can affect one another. I have to be careful of this and one should be especially careful if taking bc pills for birth control because they may not be as effective during the transition time until leveled out again. Other methods should be used in conjunction during this time.
It is a nuisance especially when you take it for other things, in my case for example when they are to control endometriosis and fibroids they help with pain. When changing psych meds dosages and to have that time of adjustment, it is really painful besides being annoying and uncomfortable.
There is research on this that you can look into on your own in how they affect one another. Perhaps you can even educate your physicians.
Hang in there.