Does anti-anxiety/depressant/OCD/ medication effect the birth controls effectiveness?

I’m starting anti-anxiety/depressant/OCD medication tomorrow but I’ve heard anti-anxiety/depressant/OCD medication can effect the combination birth control pills effectiveness but my psychiatrist says that anti-anxiety/depressant/OCD medication shouldn’t effect the combination birth control pills effectiveness. I’m getting extremely anxious and overthinking that my pill won’t work. Any insight?

^ These 2 were Planned Parenthood’s responses.

^ However this response said something different then Planned Parenthood.

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