firstly its so hard when they dont sleep and you dont get any down time.
it sounds like you have been very busy today with your little girl, so just forget about everything else that needs doing!

Hols - this age they are starting to get very active and so are their brains - so when they are in bed they are thinking of sitting and crawling. Especially if they havent been too active during the day. Teamed up with teething it can be difficult. BUt just know that bubs will go through these stages at various times.
i think pinkpalace is right, they have such active little brains at this age.
she does sound like she could be a tad overtired now, so maybe a walk in the pram could be good?
in the morning do you wait for tired signs or just put her down at 9:30? could you try putting her to bed later at say 10 when she might be a bit more tired?
could she be hungry? or thirsty? is she still sleeping ok at night?
my ds still has 2 sleeps 1-2 hrs each ( and he needs them he is so active!!) generally he is up around 7 back to bed by 10, another nap at 2/2.30 then in bed by 7ish.
i think if she is happy in her cot than there is no problem her being in there, at least she is kinda resting iykwim? but like the others said its prob best just to follow her lead..
i hope that tomorrow is better for you, and today was just a bad day. x