Interested in Language
It was me who answered the question
It was I who answered the question
Please tell me which is correct
What I believe to be more common in real life is "I was the one who..."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
Also, many speaker say It was me that answered the question, which may sound better to them than having me + who.