Gmail no longer working

I changed my password, and my gmail is fine online, and on my phone, but my Apple Mail won't recognize the password. At first, I couldn't send or receive any, then after changing some settings, as advised in the Gmail forum, I now can send, but not receive any mail. My Connection Doctor shows me connected to both Pop.gmail.com and Imap.gmail.com., yet I'm not getting any emails.

On a previous thread some people said it was fixed by just deleting the google account, then adding it in fresh. My hesitation is that I thought if we delete any email account, it will also delete every email in that account, is this not true?