Just install Authy on your computer with a master password for the personal account. No second phone needed. Or install Authy on your phone, but I can't tell if you are saying you only have a work phone and no personal phone? Or is it visa versa? I'm having trouble picturing your setup
Edit: If you already have two phones due to your work life separation, then 2FA isn't really causing you to get a second phone is it?
Edit: If you already have two phones due to your work life separation, then 2FA isn't really causing you to get a second phone is it?