So to be clear, it sounds like you arriving into ORD on BA, but departing on AA domestically. If you are arriving into ORD on AA then this doesn't make sense. Yes, after baggage reclaim and after you hand your customs slip at the checkpoint out of the hall, there is an area for rechecking baggage. There are two channels out, and the recheck area is in a cross-corridor between the two but before you get to the final door to landside. So if you are in the left channel, look right, and look left if in the right channel, it's clearly signed. They don't operate a cut off. Some people prefer to take their bags with them, but given the bus situation it's probably best not to encourage that.

If it's a few hour delay I would in the first instance go to the AA desks in T5, they are totally experienced in rebooking people there (it's all they ever do!). If you had a choice on the matter I would go to the Admirals Club and do it there, assuming you have access rights, but any agent would be able to resolve this fairly swiftly. But as ever, it's good to have the BA Holidays 24 hour helpdesk number handy, and Skype enabled for wifi on your Smartphone.

It's AA's job to do this, but you may get a better hotel option if you called BA Holidays. AA tend to use hotels like Holiday Inn Express or some such, perfectly fine for a brief night, the only problem being if there are mass irrops and their hotels are miles away. Or you can book your own (there are many decent hotels in Rosemont, very close to the airport) and claim back after the event from BA, the guideline is not to go over £200 per night but that normally isn't too difficult. Have a few hotel Apps on your smartphone (e.g. Hilton and IHG).