mail log outside of mail app

I suspect my email account has been hijacked and mail sent using my account but those emails are not discoverable in my "sent" list. Is that possible? Is there some other way of looking at a log of sent email?

Within just the last week I have been getting this message.

<< 421-4.7.28 [148.163.153.235     15] Our system has detected an unusual rate of

<<< 421-4.7.28 unsolicited mail originating from your IP address. To protect our

<<< 421-4.7.28 users from spam, mail sent from your IP address has been temporarily

<<< 421-4.7.28 rate limited. Please visit

<<< 421-4.7.28 https://support.google.com/mail/?p=UnsolicitedRateLimitError to

<<< 421 4.7.28 review our Bulk Email Senders Guidelines. x191-20020a0dd5c8000000b0052ec5f13f59si15917916ywd.263 - gsmtp

... while talking to alt1.gmail-smtp-in.l.google.com.:

Nothing has changed in my email behavior and I do not send any given email to more than ~25 recipients and never more than about 25 emails a day.

Google is not helpful, at least so far.