Don’t worry about lack of education or background in composing at this point. However, the dual degree program between Harvard and NEC is extremely selective, and I assume the double degrees at the other schools you named are too.
Do you have any live performances to use for a portfolio? I assume you are writing scores. What do you mean by formatting?
You need to know some theory, of course, in order to write down musical ideas and pieces. It helps to know music history to put your work in context. So certainly education helps. If you have already studied piano and some theory, that is great.
I do know people who went on to grad school in composing but did not do it in undergrad. I don’t know any serious concert music composers who didn’t go to college at all. Composition is actually a pretty academic field all in all and most get PhD’s or DMA’s. For one thing, those degree programs are a way to stay funded and have resources like musicians and performance spaces to develop as an artist. Composition is, for most, a matter of long term development.
Composers have more options for undergrad, I think, than instrumentalists. It is fine to go to college and study science, take the music courses you need, maybe study composition with someone and then decide about your path after graduating. It is also fine to go to conservatory and major in composition and then do something entirely different in grad or professional school.
If you want to PM me about your composing, feel free. I am having trouble getting a picture of what you are doing currently and you may want more privacy for details 
You can also go over to the music forum on CC.