Thats a quite important topic, thank you for telling us more about this. Your example was quite good, so it got more easier to understand the Problem. I although got the experience that KeePass is quite useful, you can even use it to generate passwords.
If you installed KeePass, don't forget to save the data of KeePass on a Stick or so, so the passwords are safe and protected before accidents like pc crash etc.
As long as you have as strong passphrase, the keepass DB can be safely sync'ed via cloud storage, since the data in it is encrypted. Alternatively, Syncthing can be used, allowing for cloud-less synchronization across multiple machines.