I got lidocaine at my dentist and my hands started shaking. later i looked at my lip and it was dropping will it go away and is this normal?

Yes: Lidocaine has Epinephrine added to it to make it work better. When you get a jump of epi into your system it will cause the shaking. Many people are sensitive to this, but it is very temporary. The droopy lip should go away in 4-6 hours. If it lasts more than 12 hrs call your doctor immediately.

Yes and yes: The "drooping" is just because your lips and face are anesthetized. It will wear off in a matter of hours. The Lidocaine anesthetic has Epinephrine in it, and sometimes when a larger quantity of epi enters your blood stream, your heart will race and you may shake. The effect is transient and it passes uneventfully.

Yes to both: The dropping wqas due to the anesthetic and the shaking is due to the Epinephrine in the anesthesia. I prefer to use Carbocaine without Epinephrine unless a treatment will take a long time thqat reduces the shaking to zero since there is no epinephrine.

It happens: Mostly from anesthesia given for lower teeth. It typically resolves completely within a few hours. It can be scary but really is more common than one thinks. Next time ask your dentist to use an anesthetic without epinephrine.