OP wrote that he/she was rejected from his dream schools–yes, schools with an “s” = plural as in Harvard, Yale, Princeton, & Stanford–yet then proceeds to share that Princeton University is her dream school.
Because OP initially admits that SOME of her dream schools are Harvard, Yale, Princeton, & Stanford, then switches to a discussion of just Princeton as her dream school, and OP then expresses the desire to transfer out of Brown, Penn, or Columbia,
to attend her dream school, it appears that OP has no basis for her dream school other than US News rankings.