>How can this be possible?
Doesn't seem like much to me. Do the math. Why were you expecting less? If you want to know the details, check the logs.
>Do I need to add something in my site's header?
What are you trying to accomplish?
This site is ±4 years in existing. I have never had this much http traffic and my site therefor is automatically disabled every morning and I have to enable it again.
I just thought that I can put something in the header to tell robots to go away, or will this also show the door to search engines?
You can add a robots.txt file:
But I would suggest checking the logs to see what has caused the increase. What was it before?
And what is your maximum monthly transfer and is this why it is being disabled?
I'd install Google Analytics so you can easily figure out what it is that's become so popular on your site.