My main instrument now is trumpet and I didn't start playing until I was around 14/15. I had played other instruments before, but the physical technique of a brass instrument is different than say woodwinds, piano, etc. So, it's possible.

I don't know much about the music therapy program by itself, but I do know that the theory classes pretty much start at the beginning, so you don't need to know much more than the basics. Just be comfortable with clefs, key signatures, major/minor scales (all three types of minor scales if possible), know how to build augmented, diminished, and dominant 7th chords (although they should go over those again anyway), try to learn the basics of modes and the use of roman numerals (I, V7, ii, IV etc.) and basic inversions…those sorts of things.

Also, if you have a chance, work on sight-singing (which is singing a melody a cappella after hearing the first note and establishment of a key center (generally I-IV6/4-I-V6/5-I or if you're not familiar with inversions yet, just use I-IV-V-I in the key the melody is from).

To work on sight-reading, find an old hymnal or some four part hymns online. You can find virtually any free domain music at imslp.org.

You can definitely work through sicknesses (both mental and physical) as I have. I've worked through chronic pain, pretty bad anxiety, long-term depression etc. I'm going to be blunt here…almost every person who chooses music as a profession and/or studies it in college is going to go through physical and mental problems. You have to be able to work through it…there should be people around to help support you, but YOU have to work through it. If this is really what you want to do, I have a feeling that you'll be able to work through all of it. I mean, I was supposedly going to "fail as a music major", yet I'm going back to get my doctorate in order to teach at a University. So, my point is, ignore the naysayers…it's really not so much how "good" you are (at least at any given moment as you are always getting better, sometimes only slightly and sometimes by leaps and bounds) it's how much you want it. And who you know, so make sure everyone you can get to like you likes you.