What do you call someone who is shy, withdrawn, fearful of being approached, and with little interest for or even fear of social events? Sociopath would be too harsh of a term (but close) and shy too mild.
A mild form of social withdrawal might be expressed as wallflower. According to American Heritage, he or she is
One who does not participate in the activity at a social event because of shyness or unpopularity
If the withdrawal is so significant as to avoid social contact, perhaps reclusive. Collins defines it as
living alone and deliberately avoiding the company of others
She had become increasingly ill and reclusive.
One of Hollywood's most reclusive stars.
He was reclusive by nature.
Obviously, some who are reclusive may have adopted that lifestyle for reasons other than shyness or fear, such as those who do so for religious reasons.
Some terms suggested in previous questions (1, 2) include
• private, “Secretive; reserved”
• introverted, “Possessing the characteristic property of an introvert. Preferring the internal, satisfied with self, lacking interest or comfort in social interactions”
• untalkative, “unwilling to talk; taciturn; refusing to speak”
• secretive, “Having or marked by an inclination to secrecy; not open, forthright, or frank”
• taciturn, “temperamentally disinclined to talk”
• closemouthed, “cautious in speaking”
• reticent, “inclined to be silent or uncommunicative in speech”, “restrained in expression, presentation, or appearance”, “keeping one's thoughts and opinions to oneself; reserved or restrained”
If you mean to the point where they have a general social anxiety disorder, then sociophobe, though since "social anxiety disorder" is prefer over "sociophobia", it might be better to say "they suffer from social anxiety disorder". (Specialised social anxiety disorders only apply to certain situations, and sufferers may not be at all withdrawn in other situations.
Closer to the shy end of the spectrum, you would have timid, reticent and reserved.
Introverted is often taken as being something similar to this, though its better thought of as a personal disinclination toward social events than necessarily being withdrawn or shy.
My daughter is diagnosed with social anxiety disorder. It is a disorder because it affects her ability to function (in school, in groups of people, at work). “Sociophobe” describes what she is quite well. But, probably because some people would be inclined to confuse it with “sociopath”, it is seen as a negative word for the disorder. She is not a sociopath – quite the opposite.
Sociopaths can and do deal very well with people. They can be very charismatic and have no trouble interacting with others. Con artists and cult leaders are frequently sociopaths and they are very good with people. You probably know a few sociopaths and don’t know it.
Psychopaths, on the other hand, don’t deal well with people all – though not in the fashion you are describing. Here’s an article on the subject: “Sociopath Vs. Psychopath: There is a Difference” by Jeanne Marie Kerns.¹
I think @JonHanna's suggestion is the most accurate. The others (timid, reticent, reclusive, taciturn, etc.) describe an outward behavior, not an internal state.
introverted describes an internal state, but it doesn't necessarily extend from fear or discomfort, so there's ambiguity with this choice, as well.
Closely related to sociophobe is agoraphobe, someone who has a fear of crowds and public places. This word has the added benefit of not being easily confused with sociopath.