When auditioning for musical theater, it is crucial that one ACTS the song. If you were auditioning just for a voice major, that's one thing. But Musical Theater involves not only terrific vocal technique, but also the acting and presentation of the song. It is THEATER, after all. If you merely just sing the song, that is not going to be an effective audition. You must act and PERFORM the song. You must interpret the lyrics. You can even work on a song with your acting coach a capella on the way you act it. A singing teacher will help with technique and good songs for your range and skill set, and eventually help you sing the song you have chosen technically well. You may know a vocal coach who can coach you on acting the song as well. Both aspects are important.
I do not know which particular songs you are considering from My Fair Lady, but try to avoid overdone songs, but also avoid singing and acting in dialect for college auditions.
Hope that helps.