I got a hairline fracture in my 2nd metacarpal 2 days ago, but I have badminton tournament 10 days. What can I do?

Don't play. Unless you want to risk fracture displacement and possible longterm deformity, i would advise you not to play. Although a cast could be applied i don't think that you would be able to play and splints would not apply sufficient immobilization.
Don't play. Your fracture is non-displaced (a "hairline fracture") but it could become displaced with enough force or trauma to the hand. If it displaces significantly, you may end up requiring surgery for the fracture. This type of fracture should be healed in 6 weeks, and i would suggest you avoid badminton for 6 weeks while the fracture heals.