The hospital they go to in Shameless is called County General (https://filming.90210locations.info/tv-locations/shameless/) and they use the same logo as in ER (https://twitter.com/errewatch/status/584910859140489216). Plus the diner set is where the diner and later the store was in ER as well as Fiona's new laundromat is inside what used to be the main entrance to the ER.