In real English speech, interrogative sentences end with the voice shifting higher in pitch. The question mark symbolizes this.
When speaking, you can do this with anything, to indicate that you want confirmation or to know whether it is true or not. It implies the asker doesn't believe that what he/she is saying is true, or believes/hopes that what he/she doesn't apply to them.
I'm going to school? Yes, you are going. I don't care if you are sick.
Of course the proper question form is where subject and verb are reversed:
Am I going to school?
and where the auxillary verb do is used for negative questions.
Did he say that to me?
Sentences in question form require a question mark. If they are not in question form, then they don't require a question mark and don't require the voice pitch to be raised at the end of the sentence.
I wonder if he said that to me. (No question mark)
When "questionifying" statements, because there's that implication that you don't believe the statement to be true or don't believe it to apply to you, it can come off as rude or ignorant.
I am working today? Yes, you're on the schedule. Quit playing around.