I am so sorry to hear Sadie had this spill. My primary concern is a head or neck injury from your description. Both can present with ataxia or the unsteady gait as well as the hesitation to jump down but I suspect first and foremost a neck injury.
Unfortunately I don't think you will get answers at home because this will require a veterinary exam and hopefully getting her on pain medications to control any inflammation and return her to normal.
Ideal is to have your veterinarian evaluate your dog to definitively diagnose the problem and start on appropriate medication to control the discomfort. Until you are able to do this please restrict activity (which often they are already doing themselves but that means no steps/ stairs and only carrying to go potty) and rotating warm and cool compresses on the shoulders/ neck in ten minute intervals to reduce pain and increase blood flow.
You can also do light circular massage up and down the neck and back to stimulate blood flow if this is not too painful and will allow it.
To pick your dog up please use one hand between front legs and then scooping behind back legs to avoid pressure in the middle of the back and into the shoulders. I have actually trained my little dogs to put their front legs on my forearm to minimize pressure on their backs and the associated discomfort because they too will cry out if picked up a certain way due to back pain.
Please let me know if you have any additional questions I can assist with. I hope you are able to get your little one comfortable soon, truly.
If you have more questions or if I can help in any other way, please do not hesitate to ask! If you would like to accept my answer, please press RATE OUR CONVERSATION at the top of your screen (I am not compensated in any other way). Bonuses are always welcome. Thanks!