My bedroom growing up had a slanted ceiling. Luckily it was just one direction, So there was wall space between the door and the closet - i had my desk there and book shelves over my desk. After I moved out my folks put in additional book shelves on one wall and just changed the length of the shelves to meet the slope of the ceiling. Unfortunately we sold the house after my mother passed away in 2009, so cannot send a picture. My dad had designed a paper holder - he did water color painting and had a dresser with thin wide drawers made to hold his paper - it looked like a map holder, and it went in the area where the ceiling sloped. You still had to be careful not to hit your head on the ceiling, I am 5'9" and my dad was 6'2", but it worked well, and I could see how drawers would work for you. I had put my dresser in the area too. Had to make the best of the area.
Not knowing how your room looks, and how big it is, it is hard to say if it will work. There was a show once about making use out of the sloping ceiling area, unusable space is how they referred to it. On the show they made the space into a closet, by putting a wall out to a comfortable area, and then put a couple doors in it to get to the storage area. On the wall facing out to the room they put cubbies. But one could put shelves. They were designing the the area on TV for a kid's room.