Is all of Corolla in a flood zone, as defined by FEMA? Yes, the zones are AE, VE and X
Is additional insurance required? Not necessarily...
If you are paying cash, you are generally not required to get any flood insurance.
If you are in an X flood zone, your lender will probably not require you to purchase flood insurance.
If you are in an AE or VE, your lender will definitely require you to get flood insurance.
The good news is that flood insurance is generally very inexpensive. It is less than regular hazard insurance, and much less than wind and hail coverage that most coastal homes have to purchase.
Flood insurance is underwritten by the NC Beach Plan, so the premiums are the same no matter who you purchase the insurance from. I would suggest speaking to local insurance agent, or better yet find out what the current owner is paying for their insurance.