The exact same thing happened to me, Rowan. Encumbrance becomes more and more a problem as the game progressess, it's such a pain.
What helps is to make sure you get rid of all books (you can sell them) once you've read them, as long as they're not quest items.
I also keep going to the alchemy tree in the mill basement in order to use up my ingredients for potions.
Apparently you do get a storage room in the tower, but I'm not there yet, as I've been too busy to do any gaming in the past week or two.
