I have an email for school and an email for personal use. How can I make it so that, in Chrome, when I go to YouTube it logs me into my personal account but when I go to Gmail it logs me into my school account?
Because these are both Google services that use the Google login system, I would guess that any account preference will result in both preferring the same account.
What you SHOULD do is configure a new profile in Google Chrome. Set up your personal account in one of the profiles, and your school account in the other. You can have multiple instances of chrome with different profiles running simultaneously.
Both sites use your current Google login, so I don't think you can do it that way.
Google's multi-account feature for switching between accounts is also clunky.
A solid way to handle multiple accounts is to use a separate Chrome user profile for each Google account. Each profile will have separate windows from other profiles and stay logged in to its account.
Tip: Give each user profile a distinct theme to make them easier to distinguish.
Alternative: Use separate browsers instead of separate browser profiles, e.g. Chrome, Chromium, Safari, Mozilla, Edge.