Those can all be side effects of prednisone. For me it took a few weeks before any side effects appeared, they came on gradually. I'm sure it could be quicker for others though, especially if you're taking a high dose.
So yes, it's probably normal, but that doesn't mean you necessarily have to put up with it - sometimes there are ways to counter side effects, if you ask your doctor. And be careful about driving or any other high risk activity if you're shaky.