She put on a new dress and dolled herself up.

Literal

She [topic-は] new dress [object-を] wearing dressed-up.

めかしこむ (also written めかし込む) means 'to dress up, to doll oneself up' — it implies deliberate effort to look attractive. It's a compound verb: めかす ('to dress up') + 込む ('to put effort into'). The te-form of 着る connects putting on the dress with the overall act of dressing up.