If this is a sanctioned road race, you'll have to get a bike with a drop bar. Flat bar bikes are not allowed in road races for safety reasons.

My suggestion is to check the website of the race and find out who is sanctioning it. Then check the rulebook of that organization for specifics.

ps -- I think you should go for it. Find a local skills clinic and learn how to better handle your bike. And have fun! I know women in their 50s and 60s who race -- you're not too old!