I'm 19 years old and I sleep 16 hours at a time and I also need naps. Could I have hypersomnia?

Definitely. You only need 8-10 hours of sleep at the most in a 24 hour period. If you sleep that much it does not leave much time to get anything else accomplished. You should talk to your doctor as they are many physical conditions that could cause increased need for sleep or you could be suffering from depression.
Yes but... At your age, there are other things to consider as causes of excessive sleeping. Please discuss this with a physician. Some bloodwork among other things may be required for properly ruling out other causes.