Breeze,
When you board in Chicago, they will send you to one of the coaches that go to Boston. Everyone sitting in your coach should be headed mainly to cities within Massachusetts. It's very unlikely that anyone heading for New York City will be in your coach. Normally there are two coaches for Boston and either two or three heading to NY.
When the train gets to Albany, NY it will be split in half. While you can go into the station and wander around for a bit, when they announce the train you will head right back to the same coach that you were in when you left Chicago.
Your half of the train is train #448, while the NY section is train #48.
They don't however add any cars in Albany, when the train gets split. This also means that you don't need to move your suitcase. You'll just leave it right where it's at when the train gets to Albany.