L.G.
Have you used a sling at all? Get or use one of the carriers- like a mei tei where she is hugging your back and all snug... if you keep her held and up- and she knows she can always come to you- then maybe she will let go on her own. The more you "push away"- the more she senses it and tightens her grip.
Teeth coming in probably doesn't help.
I am a stayathomemom- and my 3yr old son is pretty clingy- though in a public place like Gymboree or Chuckecheese, he is all over the place and does not seem to care where I am... it is when I am going to leave him... WELL! it is a crisis in his mind for sure.
The thing is when she decides she wants to be away a bit and explore and play, she will let you know... it takes practice and any time the seperation happens there is an adjustment period.
2nd time a sitter came over I described the sitter as a friend. "your friend is here, come say hi!" DS says, "bye bye friend" ROTFLMAO