I am so very sorry to hear about your little Enzo. My primary concern is an injury to the back not hip from your description which can be a tear/ strain but more of a concern is a herniation or pinched disc
Here is more information on this condition:
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 back/ hips in ten minute intervals to reduce pain and increase blood flow.
You can also do light circular massage up and down the 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. 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.
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