After the argument, they quickly started making up and became even closer than before.

making up 是动词短语 make up 的现在分词形式。make 意思是"做、制造"，up 表示"向上、完全"。 make up 作为短语动词，在这里的意思是"和解、和好"，指争吵后重新恢复友好关系。