You are right that we have separable and inseparable phrasal verbs. With separable phrasal verbs, the object goes between the verb and the particle.
You are wrong about hyphens, though. Phrasal verbs NEVER include hyphens. The word 'make-up' is a noun, not a verb. In fact, the most usual way to say what you want to say is 'I put on my make-up' or 'I put my make-up on', using the noun (make-up) as the object and 'put on' as a separable phrasal verb.
You can say 'I'll make you up' if you are offering to do your friend's make-up for her. But you are right in thinking that you can't say 'I'll make up you'. Why? Because if you check your grammar book under the section 'Separable phrasal verbs', you'll see that the rule is that pronouns, such as 'it' or 'them' or 'me' or 'you' have to go in the middle position, never at the end.
So you can say either 'I put my make-up on' or 'I put on my make-up'. With a complete noun, you have the choice. But with a pronoun, you have no choice. You have to say, for example, 'I bought some mascara and I put it on'. You can never say 'I put on it'. Pronouns can't go at the end.
In fact, it is not very common to use 'make up' as a verb meaning to apply cosmetics. This is mainly because 'make up' exists as a phrasal verb with other unrelated meanings. For example, you 'make up' after a quarrel when you become friends again. 'Make up' also means to invent.
I made up a story.
I made a story up.
That story isn't true - I made it up.
So, remember - no hyphens, and no pronouns at the end! I hope that helps.