"according to me is fine," but where you went wrong is the way you phrased your question. I believe it would have been correct to ask the question as follows: Is it correct to say, "according to me" ...... ........alternatively, the question could have been asked thusly: "according to me" ....is this a valid way of saying what I want to say?.............or "according to me"....is this correct or incorrect?
Me in the phrase above is an object of the preposition "to."
A native English speaker .....Have a good day!
ozkan from turkeyGuest