some dizziness is caused by your inner ear being out of whack so from laying down to standing up could be the dizzy part but shaky... also hypotension(blood pressure too low) when you get up especially if you get up fast... check your blood pressure before you get up and when you are up and feeling shaky
Low glucose levels are the most likely etiology. I know you say you "do not have diabetes", however I would like you to obtain a glucose meter, and take a blood stick. The shakiness and dizziness are hallmarks of low blood glucose levels..