Naven
Answers
Can you use a messaging app on a public or library computer?
Only a web-based one, since a public computer will not let you install anything. Sign out afterwards, and prefer a service that does not tie the account to a phone you may not have with you.
Library and public computers are locked down in the same way school devices are, and for the same reasons. A browser is generally all you get.
The bigger risk is what you leave behind. Signing out is essential, and so is not saving a password in a browser that a hundred other people use.
A sign-in that uses an emailed code rather than a stored password suits this well: there is no password to be saved, and the code is spent once.