J.S.
J.,
I have an almost 20-month old and he is the same way. I work full-time and he goes to daycare. Some days he is clingy and won't let me go, other days he runs up to the daycare teachers and doesn't look back. Same thing at home. I'm a single mom so it's just him and I in the apartment. It's not that big of an apartment, but I sometimes get followed into the kitchen, followed into the bathroom, etc. I can't have 1 minute by myself in my house until he goes to bed. And that's perfectly ok with me.
I have found that keeping him occupied takes his mind off of it. I use his bathroom when he's awake. In there is a little potty for him. I try to teach him to sit on it when I go so he can try to understand what it is for. Anyway, I find that encouraging him to see what I do works for me rather than pushing him out of the room for my own privacy. He'll grasp it as he gets older, but soon enough he'll be in his teens asking me to drop him off down the block so his friends don't see me :)
Good luck, and it will pass. It's just a phase, I think, that comes and goes.