Gmail is being rejected by the server in Apple Mail

I have several different email accounts in Apple Mail. Two of those accounts are Gmail. I had the first Gmail account for as long as I had my iMac which has been 3 years now and never had an issue. I just within the last month created a new Gmail account to add to my other accounts and I cannot get it set up for nothing. It won't let any mail in and I can't send anything out. The account I have had all along, can still generate mail to the inbox but if I were to reply to someone I get an error message that my email address at gmail.com is being rejected by the server! It goes on to give me options to edit the message or try again later.

I have tried several different troubleshooting options from changing the port number to checking the SSL box and I can't figure this out.

I have the same two accounts on my iPhone 6 and I set them both up in like 2 minutes and can send and receive emails on my phone but on my iMac, its giving me issues and error messages!

The newly created Gmail account has a triangle next to its name. I clicked Take All Accounts Online which does nothing. I also checked the Connection Doctor and its showing something completely different. Its saying account type IMAP: Connection to server and Login succeeded and its showing a green ball next to it and the ones with an issue are showing a red ball.

In the accounts information preferences, the account is enabled. The incoming server is set to imap.gmail.com. The user name and password are correct. The outgoing server is set to smtp.gmail.com. Use only this server is unchecked.

When I click Edit my SMTP list, its showing that both of my Gmail accounts are offline. Its set to use Default ports and SSL is checked in the advance tab and I have the Authentication set to None.

So to recap,

Gmail account #1 has been set up since I bought the iMac 3 years ago and has been working fine up until I created Gmail account #2 last month.

Gmail account #2 I cannot get set up at all.

Is there a better mail client than Apple Mail that I should consider using? Any other tips or suggestions to try?