Writing a character who doesn't feel emotions very strongly

Help? I'm extremely empathetic so this has been hard to write for me.
My character isn't stoic, he just literally doesn't feel much, even when it comes to traumatic experiences. Also I don't want him to sound like a more perfect being because of it, but rather more flawed because he has a hard time grasping what others might feel and sometimes tends to be very blunt and a little insensitive with words. He also thinks there's something wrong when he just doesn't get the feelings that others are having.
At the same time, he is by no means evil or bad. He has good intentions and something of a moral code. He does his best to help others, not because he feels something for them, but because it's logically the right thing to do.
So where's the line between stoicism and what I've described? Am I going about this character all wrong?

(So I wouldn't be able to help much but…. @ShadeStar might be able to. We were in a rp and her character didn't have any.)

Okay, thank you! (Now to actually convey that properly in writing)

I have a character a lot like what you described, and his older sister used to bully him because of his muted emotions and call him a machine. He developed a deep insecurity about whether his lack of emotional expression was 'right', and is pretty sensitive to people commenting on it. Being called a machine is still one of the few things that can make him really angry.
That's just some stuff I came up with on my own lol, kinda random but maybe it'll give you some ideas. Good luck with your character!