Hurricane season?

Hello, I posted in a similar sub so apologies if there’s overlap, but I am trying to plan our honeymoon and am overwhelmed and now also anxious lol. We have been looking at adult only all inclusive, preferably with private plunge pools to unwind in. Our schedules are both busy so we decided we would go August 17-22. We would like to go to either Mexico or the Caribbean and want more of a vacation than travel, but I just realized that late August is peak hurricane season and now I’m worried that will blow up our plans. Am I being paranoid? If not then do y’all have any recommendations for places that are less risky? $5k budget including flights.