Coming in from Ireland connecting to chicago

Is this one ticket on Aer Lingus (Shannon to Heathrow) and British Airways (heathrow to Chicago)?

Let’s assume this is one ticket - Shannon (via LHR) to Chicago.

You check-in for the start of your flight, your luggage is checked all the way through to Chicago (you don’t see it in London).

At Heathrow you simply make your way to your Chicago flight. There is no immigration on a flight from Ireland.

https://www.heathrow.com/flight-connections

For that matter, you go through all the U.S. formalities (security, passport control, etc.) while at the Shannon airport.

It seems I am rarely able to check all the way through online flying from Europe back to the US, perhaps this is what you are experiencing. I find it has to do with Security and to verify your passport. No problem, when you show up in Shannon, they will check you in at the counter.

For that matter, you go through all the U.S. formalities (security, passport control, etc.) while at the Shannon airport.

Not if the flight is Shannon to the UK

Sorry I should have said I am on Aer Lingus to Heathrow and British Airways to Chicago. I purchased one ticket all the way through, it has the same ticket number, but I cannot check in through to Chicago until I get to Heathrow.

Go to Heathrow Flight Connections and plug in your flight information. It will give you step by step instructions.

No passport control at Heathrow coming in from Ireland. . You cannot go through U.S immigration at Shannon. You will have to change terminals at Heathrow.

I'm guessing you can't check in until Heathrow because BA wants to check you have a valid passport.

Which airline did you buy the ticket from? Or did you buy from expedia or some such entity?

Aer Lingus flights I find for SNN-ORD, connect through Boston.

You arrive at Heathrow and follow purple line to “international connections”.