Connecting flight and Airline change

The answer is dependent on how you purchased your ticket or how it was purchased for you. If you made a single transaction with AA or another source from Chicago to Shannon and this is the itinerary they provided you, then likely you will not need to go through immigration in London, your bags will be transferred to the Aer Lingus flight, and you will be fine. To verify, I would call where you made your ticket purchase and ask about the baggage, if it goes through, then there is no need fo you to go through Immigration. If connecting at Heathrow, it is likely though that you will need to go through Security again to get to your gate. If for some reason you purchased the Chicago-London ticket, then purchased the London-Shannon ticket separately, then it gets more complicated.

Thank you for the response.
I purchased my flight thru Orbitz, as one itinerary. I will be connecting thru London Heathrow. Is there usually someone available at the gate when we arrive in London to let us know what we need to do if anything? I believe the layover is about 2 hours.

When you check you bag in Chicago they will let you know if your bag is checked through. If it is, you just get off the plane and head for the next gate. Make sure you know which terminal your Aer Lingus flight departs from, as you may have to transfer between terminals. If so, you follow the signs to Flight Connections. There are instructions on the Heathrow website. If your bag is not checked through you would have to go through immigration lines to get to baggage claim and get your bag. Two hours may not be enough time. But Orbitz should not have sold you a ticket that would not allow enough time, so I'll bet the bags are checked through and all you have to do is go to the next gate without going through immigration/passport control.

You will go through immigration at Heathrow regardless of whether your bag is checked through or not. The Republic of Ireland and the UK are part of a common travel area which means that you go through immigration when you first enter the area. You will have to go through immigration when you arrive in the UK. Normally, your bag would be checked through to Dublin but you will need to confirm that with the airline when you check in. The Heathrow airport website has a connection guide that details the steps you will take. www.heathrowairport.com/heathrow-airport-guide/flight-connections/connection-guides

The "common travel area" referred to by Laura applies only to citizens of Ireland and the UK. If you're an American, you'll have to show your passport again when you arrive in Shannon.

It is true that you will also show your passport when you enter Ireland, but the common travel area still impacts you because it means you have to go through passport control at Heathrow. If you were connecting to a location outside of the common travel area, there would be no immigration at Heathrow. Even when you are travelling within the common travel area, they are still entitled to have additional passport control; Ireland enforces this when you enter by air but not always at a land border.