The Hilton is probably your best option. There are no public luggage storage facilities at ORD any longer because of security concerns. Also, I don't think the Admirals Clubs would be willing to hold onto your luggage for more than a few hours at a time (if that). There are no lockers at the ORD clubs or FL, only open luggage cubbies.

I would give the Hilton a call and see if you can make arrangements.