Hi there! There are so incredibly many factors that go into what gets you in. As one member said, Carnegie is HEAVY acting- I can't even stress that enough. Since you're working with an acting coach, it would also likely be valuable to have them coach your songs. Since you shared your audition material, I'd like to give you some things to think about
If I Can't Love Her: great role for a young baritone! This might be slightly overplayed but I think this is easily the strongest of the songs you've listed!
Hello Little Girl: another amazing, amazing role. There's a BUT coming though...a big one. Sondheim is really frowned upon at auditions (along with Jason Robert Brown) because of the technicality. Keep it in your book, but I wouldn't advise planning to use this.
So In Love: you're talking Cole Porter, yes? This is a risky choice. I'm first going to verify that you're referencing the reprise sung by Fred, not the version sung by Lilli. The risk with singing this song is because this role is written for someone far older than you. There is so much age-appropriate material written for you, don't reach.
Some suggestions: I have no idea what your type is (you must play your type!), but you might want to look at Grow For Me from Little Shop of Horrors, Waitin' For the Light To Shine from Big River, Do I Love You Because You're Beautiful from Cinderella, Goodnight Sweet Princess from Once Upon A Mattress, Have You Cast Your Shadow in the Sea from The Boys from Syracuse, Camelot or How To Handle a Woman from Camelot... there's a lot of great music out there...
King Lear: this sounds great!
Buried Child: this is a great play and Shepard is brilliant...but this is again far too old for you. If you're really interested in using Shepard, it would be worthwhile for you to look at some of his lesser known plays- CMU in particular will appreciate finding those gems of great work done by well-known playwrights that are lesser explored
Baby in the Bathwater: you mean Baby with... ? Holy smokes...that is some choice. If you feel 100% comfortable going there, not a bad choice for a backup
I don't want to make suggestions for you without knowing your type. There are so many options out there. Play your type, play your type, play your type. And don't forget to play your natural age range.
Bradley Dean should be a great resource for you. Asking him about his audition process would be extremely beneficial to you (ask your teacher who went to Ithaca as well!). I have an acquaintance who graduated from CMU last year and he felt his successful audition there was attributed to his deciding that he was washing his hands of the audition process and was just going to go in and have fun, not try to please anyone.
I would definitely suggest adding schools to your list of auditions. If you truly want to do this, CMU is beyond a reach. Assuming you have the talent to get in, you're one of about 1200 who are going to try- it is indeed a lottery. In response to Walker1194- CMU does not discourage audition coaches. As others have said, they work with them frequently with master classes, mock auditions, etc. There are some schools that frown upon them, but this is not one of them. That being said, you will be very hard pressed to find a coach for less than $400. I am a voice and acting coach from Detroit and am trying to find inexpensive and no-cost resources for students who want to pursue MT in college- you're welcome to PM me or contact me through my site (themtproject.org) and I'd be happy to chat with you a little more...no charge
All best to you during this exciting time!