mammalicious, my son was like that too for about 3 or 4 months "seperation anxiety" and now he gradually grew out of it. I was in the same exact situation where I couldn't take a shower, couldn't leave the room for even a second but once he started to walk he got a bit better.
I also cuddle my son to sleep, at night and afternoon nap. Sometimes as they grow older they stop napping so maybe your baby doesn't want to nap anymore.