I'm 17 years old. I live in Florida and just purchased (hooray!) my
first car for $22,000. I'm covered under my mom's insurance policy as
a part-time driver on our minivan, and apparently I'm not allowed to
drive MY car until we add it to her policy. The salesman at the car
dealership said that I have some sort of ten day period after I
purchase the car to obtain insurance, and during that period I'm still
covered under my mom's (or something) policy and can drive the car.
Can anybody please verify this and provide a link to an "official"
website stating this? thanks :)

You should call the Florida Dept. of Motor Vehicles and check with them directly.