Hi! There are two primary technical reasons this is happening to you, both compounded by your specific setup of relying exclusively on public library computers and having no mobile device for authentication.
First, your Hotmail address is 18 years old. The email address itself has likely been swept up in historical data breaches. Automated bots continuously try to force their way into old accounts using lists of compromised passwords. Even if these bots fail to guess your current password, their sheer volume of login attempts triggers Microsoft's automated security system to lock the account with the exact "too many times" error you are seeing.
Second, public libraries route traffic through shared, dynamic IP addresses. When Microsoft's algorithms see login attempts coming from a public IP that hundreds of other patrons use daily, it often flags the activity as suspicious, especially if the system is already on high alert from bot attacks.
You can create a new Outlook email address that acts strictly as a hidden login portal to your current Hotmail account.
Sign in using your one-time code.
Go to your Microsoft Account dashboard, navigate to Your Info, and select Edit account info.
Click Add email and create a brand new Outlook address.
Set this new email as your Primary Alias.
Click Change sign-in preferences at the bottom of that same page.
Uncheck the box next to your old Hotmail address and save your changes