I got a 4 year old Sphynx cat 6 days ago. He’s been sleeping a lot and shaking constantly when he’s awake. I took him to the vet and he said he thinks this is nothing to worry about. I’m concerned as he is drinking quite a bit too. Any ideas of what this could be?
It is normal for cats to sleep up to 20 hours a day see How many hours a day is it normal for a cat to sleep?
Cats normally don't drink much water see How do I motivate a cat to drink more water?
Prolonged shaking is not normal in any mammal.
You don't mention the vet doing any lab work, so I have to assume he did not do any. Take your cat to a different vet and request lab work.
Other considerations; you don't say where you got the cat, but if the cat was poorly cared for in its previous home. high fluid intake and nervous shaking could be related to previous experience and poor care.