welcome to bpdr. all one can really do is work on ourselves.
her vision of her is her thing. communication, and separation of self and stuff is what i suggest you study up on. Tools over on the left side of the page is a good start.
ie...you could say "in my view, you are beautiful, i see your view is different." and leave it. no arguing, no defending. walk off.
also set good boundaries with her and everyone. " altho i love you, i cant allow this to continue. i will speak to you when you can speak like a adult--when you feel like listening to my side, etc, "/ and again, walk on.
this is very important in any relationship and is the building blocks for everyone. consistent, fair boundaries of what we allow from others.
that said, this isnt simple nor easy nor fast. it might take more posts and work on your part to understand these concepts and put them into practice.
you asked""""I want to know what I can do when one of these fights start in order to settle things in a good way.""". what you can is for you. you cant control how something will be settled but on your end. this is boundaries, what you allow or wont allow and how you choose to enforce those. it takes 2 to fight or argue. you can choose to not respond. and not allow her to disrespect you.
my guess, all it is is a guess, is she felt scared in that dress. she wanted to believe you but it frightened her and she responded in a defensive manner to deflect her feelings onto you. you took the bait, and it went from there.
that sounds like a typical exchange i have had with my H. its very important to learn to not fall into the arguing. whether things would work or not would be up to you, but also up to her. and that you cant control. only yourself.
good to meet you

jody