Congratulations on your win. While it's unusual to win so quickly so soon after beginning to enter sweepstakes, I hope you will continue this fun and exciting hobby. Expect dry spells along the way, but the win notices will brighten any day.
Paying shipping would be a downer, but having fresh flowers, that might be an incentive. Might be hard to decide. Either way, congratulations on your win. Any win keeps you motivated.
I once won a trip that the sponsor stated was in excess of $17K. I kept all records of current airfare, hotel, etc. It came to $9,887. That's what I claimed as income on my income tax that year. Never had an issue.