Don't have much helpful advice but didn't want to leave you hanging!
I am just up after being awake with out 16month old for 2 hrs last night - woke, happy as soon as being held, then just would not sleep. chatty and happy to play, but as soon as in the cot (or even bent over to put her in it!) she started with the screaming ab dabs.
The only thing I have found to work is to take her downstairs, give her a drink and something to eat, calpol (mucho teetho at the moment, think we have had 4 molars in 3 weeks) and then let her play, in the dark though, with no talking. Then back to bed, usually in her cot with whatever she was playing with and a cup of water. Eventually then, she drops off, although generally I think she plays and chatters to herself for a while. Goes against everything I thought I would do, but you do what works! If we stay in the bedroom, or I leave her to cry, she just gets so worked up, it's pointless.
I am just hoping it will pass for us eventually, I am just assuming that the teething pain isn't a problem when she is distracted, or being comforted, but as soon as awake and alone, it bothers her - which makes sense really, so I have to snap her out of it by distracting her until happy to go back to bed.
Hope you get some sleep soon!