My email service is end to end encryption,
Unfortunately, when logging from an untrusted computer (your company's here) this does not mean much:
- The company may have installed the company's certificate in the trusted root of the browser you use and be proxying all the traffic through a server which essentially performs a MitM attack.
- The company may be observing the programs' memory, logging your keystrokes, ...
which means it does not store password or reset password.
You should be able to reset your password, end-to-end encryption does not preclude resetting passwords. Select an e-mail provider/technology which allows it.
On the other hand, if you operate from an unstrusted computer, password-protecting a private key is not as effective: since the company may access any program's memory, they may access your private key after it's decoded with your password.
I can't shift the screen.
If you are worried about your team members seeing your e-mails, then you might want to bring this point to your boss; especially if they are used to send you confidential e-mails (such as discussing the performance of some of your team members, or other personal information).
However, this should have no impact on your passwords: it should never appear on screen.
In light of the fact that your company may very well be "spying" on you, and possibly legally so depending on your jurisdiction:
- use a work-only e-mail account (do not leak your personal mails/discussions to your company)
- use a work-only password (do not leak your preferred password to your company)
If you wish to secure said e-mail account (to prevent others from perusing your e-mails or sending them in your behalf):
- rotate your password regularly
- use two-factor authentication, if available