Re: teething or an allergy?
Since she's obviously teething, and the symptoms you're seeing coincide with the teething, I think this is (you guessed it) teething. If it was allergy it probably would have shown up previously. Also, the watery, green poop and diaper rash are often a byproduct of teething, since the baby produces copious amounts of drool which have weird effects on poop.
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"