It not "normal", but not necessarily uncommon. Oral contraceptives change your hormones, and can therefore certainly effect your mental health. Just like they can Be used to help regulate PMS Related mood disorders, they can also contribute to them in other women.
Talk to your doc. A different pill with a different estrogen level and/ progestin can make a world of difference.
I took one pill years ago that turned me into a stark raving lunatic monthly. Had never had trouble on pills before that, and didn't after, despite changing brands many times over the years. It was awful, so I understand what you're going through. Just get off this pill - it doesn't mean it will happen with all pills, if you find that OCs are the best contraception for you. There are other options.