If this problem pertains to gmail alone. This may be of use: https://support.google.com/mail/?hl=en#topic=7065107

I'm just unsure on what it is you're trying to do in particular in relevance to Mozilla Firefox.

Thank you. I clicked on the link, got Add another email account to the Gmail app on the screen, Clicked on Add an Account below that, and followed the instruction. At Item 3 there is no arrow to the right of my user name. There is, however a circular icon.

For that particular guide, that is for the Android App. I'm assuming you want to create a new account if so refer to this: https://support.google.com/mail/answer/56256?hl=en&ref_topic=7065107

If you'd like for further assistance, and probably more helpful response. I would click https://productforums.google.com/forum/#!forum/gmail and make a ticket for them in particular.

I want my new mail account to appear when I am in Firefox .

I want my new mail account to appear when I am in Firefox on my computer

If you use extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) that can block (wanted) content (e.g. Adblock Plus, NoScript, Flash Block, Ghostery) then always make sure such extensions do not block (wanted) content.

• make sure that your extensions and filters are updated to the latest version

You can try these steps in case of issues with web pages:

You can reload web page(s) and bypass the cache to refresh possibly outdated or corrupted files.

• hold down the Shift key and left-click the Reload button
• press "Ctrl + F5" or press "Ctrl + Shift + R" (Windows,Linux)
• press "Command + Shift + R" (Mac)

Clear the cache and remove the cookies from websites that cause problems via the "3-bar" Firefox menu button (Options/Preferences).

"Clear the cache":

• Firefox/Options/Preferences -> Advanced -> Network -> Cached Web Content: "Clear Now"

"Remove the cookies" from websites that cause problems.

• Firefox/Options/Preferences -> Privacy -> "Use custom settings for history" -> Cookies: "Show Cookies"

Start Firefox in Safe Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration is causing the problem.

• switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Appearance
• do NOT click the "Refresh Firefox" button on the Safe Mode start window

• https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-using-safe-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems

Thank you. This is much too complicated for my old brain. I'll write to my granddaughter and ask her to set it up for me.