Is always shaky feeling normal after feeling an earthquakes? Like trauma or something?

No. Multiple exposures may be a trauma, or some fearful situation. One may need counseling to clarify and stabilize mechanism to deal with this.
Yes. It is a normal reaction after a trauma or a stressful event to feel that way due to release of certain substance into your blood stream (adrenalin); however if this feeling persist longer than usual, or for no apparent reason you feel " shaky and anxious", you may be developing some sort of anxiety disorder.