12 week old kitten shaking after Rabies vaccination

When we first got home from the vet 12 hours ago, my baby "Rémy" was totally fine. Running around as usual (he's a spazz cat). Then, I came home with some friends 6 hours later and he was not being social not paying with his favorite toys. I assumed he would have so much energy after being alone. He's never been shy. Not even to the vet this morning. Well, he's been super lethargic, even towards me. And when I've held him he's been shaking!!! Not like tremors, but as if he's cold. He's been eating/drinking and his ears aren't hot, maybe cold if anything. I'm somewhat panicking! I'm a new pet mommy and I hope he won't pass away when I fall asleep tonight. Is this normal? The shaking?

Thanks!

Just an update-- within hours of this post he was back to attacking my face while I was sleeping. So, he went back to his normal self

Hooray!  So glad Remy (love that name!) is back to his old self   Some kittens will have a reaction to the vax, but symptoms should resolve within 24 hours.  And, happily, they did.  Not sure if your vet used the Purevax formulation, but it is reputed to be the safest.  You can always ask for it in advance next time (most vets will order it if they don't already carry it)    And, if you weren't already aware, the best place for vax is the tail, a hind leg being second best.  If a lump forms at the injection site, contact your vet.  (It probably won't.)

Having gotten that out of the way...  What a beautiful baby!    Congrats on your new furry bundle of joy