Can I find out on which website I got my Litoshi address?
Look at a list of Litecoin web wallets to see if any one them sound familiar to you:


LiteVault - Online Litecoin Wallet; private keys encrypted locally
Hive Web Wallet - Online BTC/LTC wallet; private keys encrypted locally
Liteaddress.org - Litecoin address generation tools (BIP38)
Reddit LiteTip Bot - Give and receive Litecoin tips from reddit users
Coinkite - Coinkite is a web wallet with merchant services, Point-of-Sale 
terminals and debit cards. 
CoinWallet.co - Online wallet
Harborly - Online wallet that can be linked with any US bank account
HolyTransaction - Online wallet, multi-currency support
Celery - Online wallet
Cryptonator - Multi coin wallet


https://litecoin.info/Category:Services#Wallet_services

If you are able to locate your account, please send your LTC to an offline wallet with a strong password that you do not use on multiple sites. 

Web wallets are not the most secure and your practice of reusing passwords on many websites is a horrible security practice.