Sounds like hypnic jerks to me from your description. Usually, a benign phenomenon (should go away on its own) happens when you are transitioning from awake state to sleep state. Usually, triggered by emotional or physical stress, sleep deprivation or too much caffeine or other stimulants.
Not associated with anything in the vaccine but associated with the anxiety and stress associated with vaccination, can be associated with fever If you have any. Further history is needed to identify that.
Next Steps
Take a walk. Sit upright, read a book in a dim yellow light. Ease yourself with some breathing techniques if you know. Try over the counter melatonin 3 mg, make yourself a non caffeinated green tea like chamomile.
Then try sleeping again when you feel drowsy.
if it persists you might need an anxiolytic for which you need to consult for a prescription.
if it recurs and persists don't hesitate to consult.