Why is my phone emailing spam?

Last month I received bounce back emails or auto-reply on emails that I did not send. I checked my Sent Mail, and nothing out of the ordinary showed up. I checked my Spam folder, and that's when I found a couple of Mailer-Daemons, and the "sent from my iPhone" signature. I deleted the account off my phone, revoke and regenerated passwords for my devices, added the account back onto my phone, and all was well for about a month. Today, May 22nd, I have had the same exact experience happen.

So far I have deleted my gmail account from my phone, changed passwords, revoked app on all devices, and haven't added anything of it back.

Also, I checked the "details" on my gmail account, and found that my account was currently logged into another session. I signed them out immediately, and within 15 minutes I received a weird/spam text about a cruise. I didn't open it but deleted it right away. I'm not sure if this has anything to do with my email problem, but thought it was worth mentioning.

Long story short, can anyone help?