Why are you looking to change majors? It’s ok of course but what in your background supports that major, if anything?
Same as an earlier thread of yours, it does seem you haven’t given your school enough of a chance, at least partially due to a perceived lack of prestige. Regarding NU and Chicago, these schools aren’t similar in vibe (which suggests a prestige rather than fit focus), and it sounds like NU fits your new wish list better.
Not getting accepted to NU initially isn’t a huge barrier, especially as you wouldn’t be reapplying to Medill, so apply and see. I know more than a handful of students who NU denied for first year but were accepted as transfers.
What other schools accepted you last year?
Would you stay at your current school if a more prestigious school doesn’t accept you as a transfer (and of course is affordable)? You do need a backup plan.
You are going to have to give more details here, and it sounds like you have other financial
Issues happening, based on a prof helping with fee waivers (fee waivers for what, have you submitted transfer apps?).
A $40k EFC suggests you would need at least 50% discount (aid) at schools like NU and Chicago, which is not insignificant.
What can your family pay per year?
Until you give us more clarity, I don’t think schools like American or George Washington (good suggestions) will be affordable.
Regarding outside scholarships they are difficult to get and typically time consuming to apply for, relatively smallish amounts, and non-renewable. Many meet full need schools like NU and Chicago will reduce your financial aid packages for outside scholarships. They will start by eliminating self help $ in the FA package, but if the outside scholarship is large enough, they will reduce institutional grants.