For first time ever my dental hygienist used a high speed drill while cleaning my teeth (very stress inducing). is this permitted in florida?

Drills don't clean teeth, they polish teeth. How do you know it was a high speed drill? A Cavitron ultrasonic machine is the most common instrument used. Unless you had such thick calculus on your teeth that a Cavitron couldn't remove, that a high speed drill could be used to soften up the material. All these methods are standard if necessary in all states

You can ask your hygienist to use a different way to clean your teeth, If you do not get satisfactory response you can go to a different dentist.