While many people are sensitive to physical contact, an actual fear of being touched can lead to a host of difficulties. It can come about from a past trauma, learned experiences (through growing up in a family where touch was discouraged or punished), a physical sensitivity, or a mental health condition, to name just a few possible causes.

Backing away from handshakes, kisses, or other cultural greetings
Sticking to the fringes of crowds
Avoiding romantic relationships
Not eating certain foods due to their texture 
Not participating in contact sports, dancing, and other activities that require touch
Difficulty making new friends
Only being able to wear certain kinds of clothing that don't chafe or irritate the skin
The character keeping their hands in their pockets
Flinching away from physical contact
Stiffening when hugged or patted
Being comfortable with touch from a select few people
Becoming irritated when they're hugged or touched without consent
The character wearing a badge or sticker that tells people they're not comfortable being hugged
Sticking close to people who know the character and respect their boundaries
Avoiding doctors and dentists

The character feeling uncomfortable when their personal space is invaded
Desiring sex or other forms of intimacy but being unable to endure the physical contact
Distrusting men or women (if this was part of a traumatizing event that spawned the fear)