Why not just go with anxiety? Many people have anxiety, it can affect a person in unique ways without them necessarily being awkward. (I have anxiety, I'm shy, and I'm usually not awkward)
It's normal to love the people you're close too and have time to get to know them. Caring about and prioritizing their feelings while having little empathy for strangers can just be part of his personality. Also, caring about strangers/people you don't know well requires internal energy, if he's dealing with anxiety, he might intentionally shut himself off from unnecessary people things, because he can't cope.
Basically for an anxious person, being numb and shutting down can be coping mechanisms.
Maybe you're making him too emotionally illiterate? While the reality is that emotions are very complicated and can be affected in complex ways, I foresee issues conveying "I get that you're sad, but I don't know what sad actually is, so I don't want to do anything to make it worse!" Conversely, it's way easy to convey, "You're sad! I understand that, but I'm anxious I'll some how make it worse, so I'll do/say nothing!"
I think it's easier for an audience to empathize with being anxious and not knowing what to do, rather than saying he doesn't experience sadness. Especially since you've said he does experience emotions, he just has trouble connecting the dots. (Right? I'm doing my best! I'm no psychologist!)
And if none of that is helpful, just ignore me. 
Edit: Alternatively, just write him the way you imagine him, and worry less about the details. 