First thing, exchange addresses cannot receive airdrops (if this is related to any tokens from any ICO). If you want, you can use an address from MyEtherWallet. Secondly, no, your address is not compromised. You shared your address but not private key (never do that ever). On what basis are you thinking that it might have been compromised BTW? No need to request an address from Bittrex as it's on their end, you don't hold (possess) the private key of that address. In order to receive any tokens via airdrop that are ERC20, you need an ERC20 compatible wallet and MEW is one of those that supports it, why not use that instead?