Welcome to e health!! Glad to have you.
You're right, our hormone cycles during the month and that causes mood swings at certain times.
For most women, birth control will take the normal ups and down of our hormones and make them more of a flat line. However, they don't always get quite to flat, sometimes they are just wavy- in this case, you might still have mood swings at certain times, because your body still cycles. So no, it's not imaginary. But if you're still having pms on your pill, it might get better if you switch to a different pill. If you are interested in that you can talk to your doctor.
Also, when you go on your placebo week, you have a sudden withdrawal of estrogen and progesterone, so that could also cause mood swings in some women. And the reason it cases low sex drive or depression is also hormonal- but again, switching to a different pill might help with that. And yes, your menstrual cycle could still be effecting your sex drive and mood/depression.
Also, many medications for depression can cause low sex drive, if you are on any.
I hope that helped...