Can I change a spelling in my name in school !?

No. They have to go by the way it is spelled legally. For legal purposes, obviously. Otherwise their records would state that Nicki Whatever attended classes and so on and not Nicky Whatever. That would then mean you could be counted as absent or not having gotten certain grades or anything else because everything would be attributed to this Nicki person and not to you. So unless you legally change your name then their transcripts have to reflect your proper legal name as it now is.