OK, so I've traveled a lot, with stuff I can't let out of my sight. Have had to do some weird re-checking, like in Germany on the way to Ireland, and have been felt up by many security persons because of the stuff I have to carry with me... Germany was the worse. Only my Doctor has been more personal in a clinical setting....
If you're transiting through Dublin you might need to recheck your bags. It all depends on the agreement your airline has at that airport with TSA. Dublin does allow you to clear customs there, so when you arrive, you're OK in the US and don't have to reclear,
IIRC.
My experience with carry on is it depends. Some flights have very small overhead bins, and being even 1 or 2
cm over might make it so your bag doesn't fit.
Get something with soft edges. And lots of foam. That'll let you cram it in the overhead if necessary. Plan on buying glue and spending time re-gluing when you get here. You'll be fine that way if you get a bag that's close on the linear inch limit for carry-on.
Also, if available, pay extra for early check in. Be a charming sweetheart to the folks letting you on the plane. Gate check as a last resort. If you have stuff you can't stand the idea of rebuilding, create a "minibag" inside the larger bag that you can pull out if they insist on you checking it.
Overall, good luck! You can buy more underwear when you get here!