Great! It sounds like you will have many options, not everyone is so well prepared. I’m sure you are not assuming that most universities have no audition requirements, many do. I think Compmom and I are, in our own ways, pointing out that there are many routes - conservaory to LACs to large and small private and public universities. Each will have its own admissions requirements, rules regarding double majors, ease of access to teachers for non-music majors, etc. But, I’m sure you are aware of this and are researching the Music Department pages of places that might be of interest ro you.
Please note that many musicians cringe whenever an instrumentalist refers to the instrumental repertoire as “songs”. Singers sing songs, instrumentalists play works, pieces, repertoire or specific genre such as sonatas, concertos, etudes, etc. I don’t mean to belittle your post, but many who hear the term “song” used in reference to an instrumental work will assume a lack of higher level or serious training - obviously not true in your case. Please forgive me if I seem rude in mentioning this, I don’t intend to be offensive, just pointing out the terminology a professonal musician is likely to use and to expect to hear.