Since all our passwords are stored in our home computer and we cannot access them offsite.
With KeePass you can install it on multiple devices and copy your database between devices. You can even carry the database around on a USB stick which you could plug in to other devices. If that's too much effort for you, then you can use something like Bitwarden and automatically sync your passwords across devices using either their server or hosting your own server.
Some people may suggest to install the same password manager on another computer but then most public computers will not allow this facility too.
You should never be logging in to
anything on a public computer. You have absolutely no idea what kind of security (or lack thereof) is present, what malware is present, if the owner/admin is monitoring your keystrokes or screen capturing, what their internet security is like, and so on. If you log in to anything on a public computer, you should consider it immediately compromised.