Like most US carriers, Northwest allows each passenger one piece of carry-on luggage that can fit in the overhead compartment, and one "personal" item that can fit under the seat in front of you.
The bigger piece of luggage can not exceed 45" when all 3 dimensions (length, width, height) are added together. If you are taking a suit bag on the plane, it has to fit in the overhead and not exceed 45". That does count as your one piece of carry-on luggage.
Don't laugh to much. On our last cruise room was very tight. We always carry to much, and I was determined to cut back. Since I never cut back on camera gear clothes was the only option. Instead of dress shoes I took a nice pair of black leather waling shoes. I used them daily. I cleaned the to a nice shine with Armor All Leather Care Wipes. I will never go back to dress shoes on a cruise.
I always carry my suit in the checked bags
I've got several pairs of deck shoes and on our last two family cruises I didn't bring dress shoes either. A dark pair of the deck shoes look good enough with a suit so I went with them. They worked fine on the casual nights too, so I wore them on the flights, on the cruise every night, and back home again. Made things easy for me. Just those shoes, a pair of running shoes, and some flip-flops.
Shoe selection is always a problem. I bring a Tuxedo and deck shoes even black ones would not work so I wear my dress shoes. I pack the Tux carefully in the suitcase. If you fold it well it should shake out OK. Between the Tux and the Kilt (which gets rolled and uses surprising little space) I barely have room for other stuff. Lucky that a pair of shorts, swim trunks, a few polo shirts, lots of underwear (always new for a cruise) doesn't take much space.
Of course if you really are finding space an issue try renting a suit from the cruise ship. I know you can do it on Carnival, you need to arrange in advance and can include shoes.