You'll be fine. If you booked it all as one ticket, you'll have both a checked bag and a carry on bag for the entire itinerary. The problem you've spotted is just part of the torturously stupid way Aer Lingus displays itineraries. Something like the problem you have encountered comes up every few weeks, so know you're not alone. On Transatlantic, everyone flying Aer Lingus gets a cabin bag so the online itinerary doesn't always show it as included. On European routes, only certain customers do, so they specifically show if the fare includes a bag or not. It says it if you wade through various FAQ pages of the website, but the online itinerary seems to be crafted to show the information in the most confusing way possible and often is just flat wrong.

Rest assured that they're much better on the air and on the ground than they are at customer service and IT stuff, and you should expect to have a pleasant journey. Come back here if you have any other problems - most of us fly with them regularly and can help you navigate this sort of stuff.