This is a well-known fraud. Do not send them any money. You have not won a sweepstakes.
Scammers always want you to believe that you can be picked out of thin air and become a contest winner. You can't. You must always enter a contest to win it.
Lottery winners are paid out of the proceeds of lottery tickets. If you don't buy your ticket you can't win, and you must present a valid ticket to claim your winnings. US lottery tickets cannot be sold on line. It's against Federal law. You must buy them in person from agents at specially designated locations.
Sweepstakes winners must complete an entry form and sign up for the contest. Sweepstakes also require you to submit your half of the entry form as proof before you can claim your prize. Your half of the form with your winning number matches the information the company has on the other half which was pulled from the drawing.
Finally, when you win a real contest, the money already belongs to you. So you NEVER have to pay anything up front to receive something that's already yours.
In any legitimate contest, if there were indeed any transfer expenses, the contest would simply deduct it from your money which they already have and just give you a check for the rest. But with a scam contest, if you notify them, they will ask for money up front for taxes, insurance, courier or transfer fees, or they will give you a partial check and ask you to deposit it and use the money to pay a third party. There's no need for any of that with a real contest.
The up front fee is the #1 sign of a contest scam.
Report the scam to the FBI online at their Internet Crime Complaint Center at IC3.gov.