I agree with Ryoko-san and I also think the way to say "Hair and makeup for my cousin's wedding" is 「 いとこの結婚式のためのヘアメイク」. However, Samantha-san is trying to describe a particular photo, so the phrases can also be "いとこの結婚式でしたヘアメイク( hair and makeup which were done for my cousin's wedding)", or "いとこの結婚式用にヘアメイク中 (I am doing my hair and make up for my cousin's wedding)". Photo is a moment, so various descriptions are available(*^^*)