I think the most important thing you do right now is put your baby somewhere safe, and have a nap yourself.
Sleep deprivation is gad awful!
As for your baby, I do t think there's a single baby who hasn't taken a tumble and been perfectly fine. I wouldn't go to the GP, she's fine if she hasn't showed any symptoms by now. Relax.
Most babies are pulled out of earthquake rubble completely unharmed, so I think you need to be calm- they're designed to survive most anything!
Can you sleep beside her on the bed, while you feed her, as it's safer - the risk of sofa sleeping is higher and unacceptable IMO, as it's too small a space.
Look after yourself first - you need to make your own sleep needs a priority.
There's a reason why you have to fix your own oxygen mask first in an airplane!! Your needs are actually greater than your baby's at this point. And sleep is a MUST! Get the help you need to enable you to get a nap.
And get a bouncy chair and a sling- you need to be able to go to the loo and eat, so organise yourself for the long haul.
Crying for a half a minute when you rinse your hair in the shower won't kill her if she's laying safe on a towel in the bathroom with you.
Same as when you're fixing yourself something to eat. Just put her down on a blanket beside you and put some music on while you eat.
You need a break to eat and look after your needs.
Look after yourself, first and foremost: your baby will be fine being put down for a few minutes, and the better for a happy rested and calm mummy.
Congratulations btw. Becoming a mum is a total mind wreck, and you're not alone!