Hi Kenrick, my name is Neil, and I'm an Outlook user like you.
Since you are using a shared computer and your host has the only account on what sounds like Outlook desktop App, I suggest you retrieve your emails using the Outlook Web App.
This is the Outlook website where you can log in to your account, read your emails and then log out again. This doesn't involve leaving anything on the computer like your email account and will therefore not interfere with your host's own email account.
Also, you can access this website from a mobile smart phone too. This means that you would not need to access your hosts computer at all if you have a smart phone.
To access the Outlook website (on a computer or phone), click on this link: https://outlook.live.com/
Once you are there, click on Sign in and insert your email address and password into the boxes when asked.
After signing in, you will be looking at your emails Inbox.
If you have forgotten you password, please go to the following link to reset it: https://account.live.com/password/reset
If you cannot reset your password for any reason and need to recover your account, you need to go to the Account Recovery Form page and fill this out. Here is a link for help with filling this out, that includes a link to the Account Recovery Form too: https://support.microsoft.com/en-us/account-bil...
I hope this helps.
Kindest regards,
Neil