What is the feeling called when you think someone is following you but really isn't?

Solution 1:

I think the word you are looking for is paranoid or paranoia

paranoid : medical : of, relating to, or suffering from a mental illness that causes you to falsely believe that people are trying to harm you

: having or showing an unreasonable feeling that people are trying to harm you, do not like you, etc. : feeling or showing paranoia
_{^{Merriam Webster}}

Solution 2:

In U.S. football—a sport where the quarterback is a constant target of onrushing defensive lineman and sometimes also of blitzing linebackers and safeties—a quarterback may sometimes get rid of the ball before he needs to, because he senses an approaching defensive player who isn't actually there. This phenomenon is sometimes called "hearing footsteps" and it may lead to a case of "happy feet" by the quarterback—repeatedly prematurely bailing out of the protective pocket created by his offensive linemen to run for his life.

So if you suddenly feel as though you're being watched and followed, someone may actually be tailing you—or you may be having little flashes of paranoia that cause you to think you "hear footsteps" where in fact you do not.

Solution 3:

In various sources, it is mentioned as sensed presence or sensed presence effect.

Have you ever had the sense that you were not alone, that another person, perhaps menacing, was in the room with you? And yet, when you look around, no one was there? This is a common experience, which researchers call a “sensed presence.” Neuroscientists hypothesize that this common experience likely has a neurological correlate – meaning that activity in some specific part of the brain is responsible for generating the sensation of a presence.

^{http://theness.com/neurologicablog/index.php/who-goes-there/}

And recently, it is discovered that the brain region which is responsible for this phenomenon is angular gyrus:

Do you ever get the feeling that someone is behind you and you turn around to see no one there? Scientists believe that they have found an area of the brain that is responsible for that creepy feeling. It is called the angular gyrus.

^{http://blog.lib.umn.edu/hutch213/myblog/2012/02/out-of-body-experiences-and-the-ghost-behind-you.html}

In plain English, I would call it an eerie sensation or eeriness.

eerie (n)

Inspiring inexplicable fear, dread, or uneasiness; strange and frightening.

Suggestive of the supernatural; mysterious.

^{http://www.thefreedictionary.com/eerie}