Unlike other posters here I disagree that it will not make a difference that you are shy. The LOR’s you get should talk about who you are and that will be difficult if the writer doesn’t know you that well. Brag sheets are worthless unless they convey something more than you can find on other parts of the application. My DD conveyed to all her LOR writers (and yes they asked for brag sheets, as she went to a public HS) that this was not a brag LOR, these LOR’s needed to talk about who she was, what her character was like, how she interacted with others. Her academic prowess was already displayed by scores and grades, no need to repeat that she had a 5 on a particular AP test, these things are already known. You are right to find schools that don’t rely on LORs if you don’t know your teachers that well, many of the schools already suggested are fantastic schools that would be happy to have you.