This is an unproven theory. Chrome is probably the browser you normally use. Do you always 'Sign out' when leaving Webmail? If you don't, sessions accumulate (fact). Over time, this might cause unexpected results. When you changed browser, sessions hadn't accumulated... yet, so Webmail functioned normally. To clear accumulated sessions, open Webmail using Chrome:
Webmail: Settings 
> All settings ... > Security > Sign out from all devices
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If that fixed your issue, please let us know. Otherwise, here are some Chrome things to try, one at a time. (If you're familiar with Chrome settings, just do the bold stuff). When testing, close all Chrome browser tabs and re-open Webmail.
- Verify you're using this Webmail URL: https://myemail.cox.net/
- Verify you have the current Chrome version. Click the three vertical dots in the upper right > Help > About Google Chrome
- Open Webmail. Reset site permissions. Click the lock icon left of browser address bar > Site settings > Reset permissions
- Clear browsing history, Cox cookies and cached images and files. (With Chrome settings still open) Privacy and security > Clear browsing data > Check 'Browsing history', 'Cookies and other site data' and 'Cached images and files' > Clear data
- Disable extensions. (With Chrome settings still open) Extensions. (Disable all extensions. If that solves the issue, re-enable extensions you disabled and and disable each, one at a time, and test until you find the extension causing the issue).
- Let us know what fixes the issue... whether it's one or more of the above or something else.
