“match”?
You are confused.
Every college awards its own money according to its own formula. The same family can expect to get different aid packages at different schools. You should have ZERO expectations of a match.
IF you can get someone at Georgetown to agree to review your aid package, then perhaps the amount you’ve gotten from another school may be relevant.
But there are no guarantees that Georgetown will care what you got from USC. None. If you got a 35K need based package and your parents finances are straightforward (not divorced, don’t own a business, etc.) then the aid calculator from Georgetown ought to be reasonably accurate for you.
What did those number say?
and where did you get the crazy idea that financial aid is some sort of poker game?