If you never receive payment, every single photo you take is your intellectual property. The law says so!
The makeup artist may had contributed an idea or theme, but one cannot copyright/trademark/patent ideas or themes for photoshoots. They contributed their time, but so do you.
They need you, not you need them. In other words if you don't release photos to them but only use the photos for yourself, nothing they can do, legally.
Singapore no need model release, only USA. Good to have, but no need. You can use for your portfolio.
The MUA does not know what she's talking. She tried to play boss and bully you, don't let her. You have your artistic right to edit your own creative work, who the fartface is she to restrict your freedom of expression?
My advice is to send a firm but polite email explaining the situation and legal stand to them, thank them for their time but you won't be releasing photos to them.
Case won't entertain her. She has to initial a civil sue against you if she like, but she won't win. No lawyer wanna fight a losing battle and bring down their own name. I don't think she can even afford the initial consultation fee, much less court fees and the whole shebang.
What a naive MUA who messed up.