Strange behaviour in mail and safari - security problem?

I use a MacBook Pro and I'm worried about security after something that just happened.
I'm not at all technical, so please forgive if my query is clumsily described...
I had Safari and Mail open while I was working on something else. I had my Google Calendar open in Safari.
I went to Mail to check if I had any emails, and noticed that the columns in my inbox viewer had rearranged themselves, and all the columns - most of which I don't normally have open - were on display. I opened my "sent" box to see if the same thing had happened there, and it appeared completely empty - i.e. there were no messages on display.
I opened a couple of other mailboxes, and they were full but all the columns were displayed, like my inbox. When I eventually went back to my Sent box, the messages had re-appeared, and the correct number of columns were displayed, but in a different order (l to r) than I had previously arranged them. When I sent back to my Inbox, it was the same as the Sent box.
Just then I got an error message in Safari, saying "You have been logged out, possibly in a different window" - whatever that means.
I had to re-enter my username and password to get back into my Google Calendar - but then I started getting nervous.
Should I be worried?