It’s pretty clear that Sheldon is on the Autism spectrum / Asperger’s.
I can’t believe nobody pointed this out before.
He’s pretty far out on the spectrum, too, though what they call “high-functioning.”
So his social interaction peculiarities are not necessarily a reflection of his inner self, but more a consequence of his inherent inability to “see” what others see.
There have been many clues throughout the show that he is at heart a sweetie: he loves his mother and Meemaw to death, despite having nothing whatsoever in common with the, and he’s always there to help Penny when she needs him, although generally in an annoying way.
The “not wanting to be touched” bit is of course classic autism.