There is a makeover, in English. This could be literal, for example fashion-related (make-up, a restyling or "un relooking" in franglais), or figurative, like some sort of transformation. The verbs are to give someone a makeover, or to make somone over.
The song is about attraction, and wanting to transform oneself in order to please the other person.
[I'm] changing myself just to stand alone in your eyes, in your eyes
Pull me in, take me out, make me over.
Je me change juste afin d'être le seul devant tes yeux, devant tes yeux Aspire-moi, expire-moi, transforme-moi.
Juste pour t'en donner une idée - c'est mon interprétation, et risque d'être très grosso modo
In Don't Make Me Over sung by Dionne Warwick, she says: "Accept me for what I am, accept me for the things that I do", so it is as described above by GEmatt, "Don't make me over" here means, "don't try to change me".