Hey Artemide,
Sorry to hear about your second PC. 
Sharing a PC would be fine if you both have your own account. If you do (and depending on how well you know each other), do try to make sure that you log out of your account (both in-game and the Battle.net app.) when you’re done playing to avoid any issue or “prank”. Having an Authenticator on your account and on your phone could also always help.
Other than that, you should be good to go. 