A company doesn't have to give you sick pay, they're not legally obliged unless stated in your contract.
They'll be asking for a doctors note just as proof you're ill, won't be any other reason. You've been off for two weeks and say you're leaving on Friday, IMO, you won't get paid for those two weeks, even if you hand in a sick note.
All you'll get paid for the month (if you're paid on a monthly basis) is how many hours you've worked and/or holiday pay.