Diagnosis for consistently preceiving mild displeasure as personal threats? I'm aware the site does not accept self-help questions, but I think this one can be answered in a situation-independent way. So


Is it possible for someone to exaggerate mild displeasure (justfiable or unjustifiable through social norm) as personal threats? 
And what does it mean?
Short answer
Paranoid personality disorder and social anxiety disorder come to mind.  

Background
Perhaps you are after paranoia, which is thinking and feeling as if you are under threat even though there is no (or very little) evidence that you are. Paranoid thoughts can also be described as delusions. Paranoid thoughts can be exaggerated suspicions, e.g.., someone made a negative comment about you once, and one inflates that rather irrelevant remark to a full-blown hate campaign. 
Thanks to r0berts' commentary below, I wish to add that, according to the DSM-IV-TR, paranoia in itself is not a diagnosis. Instead, it is diagnosed in the form of paranoid personality disorder, paranoid schizophrenia (a subtype of schizophrenia), or the persecutory type of delusional disorder. paranoid personality disorder may be what you are after in specific:



  Paranoid personality disorder is generally characterized by a
  pervasive distrust and suspiciousness of others. Sufferers often
  believe that other people’s motives are suspect or even malevolent.

Paranoid schizophrenia is characterized by predominantly positive symptoms of schizophrenia, including delusions and hallucinations. Without going into detail, schizophrenia is probably not what you are after.
People with persecutory type of delusional disorder believe that they (or someone close to them) are being mistreated, or that someone is spying on them or planning to harm them. Likely also not what you are after.


Another disorder that comes to mind is anxiety disorder, and specifically 


  social anxiety disorder, or social phobia. This is
  characterized by overwhelming worry and self-consciousness about
  everyday social situations. You fixate about others judging you or on
  being embarrassed or ridiculed.