I have a text file with all the passwords I use for my web accounts.
That's very insecure! You should seriously consider getting a password manager. I use KeePassX on Linux (for Windows it's called KeePass), but there are other options too. It's worth the time to set it up once, and add all new passwords in the future.
See for instance
The Five Best Password Managers.
I wouldn't trust a website for this. My password manager does this for me.