Similar problems here. I'm somewhat OK with people looking at my face when they are talking to me, but it's embarrassing and feels rude not to look at them back, which causes the main problem. I really try to maintain eye contact with people, but it feels very unnatural and forced... Makes me feel like I'm staring instead of looking. That's when other people's eyes begin to feel piercing as well. Sometimes the other people looking at me feels so uncomfortable it makes me wish I'd vanish in thin air.
It's gets kind of ridiculous, to be honest. Instead of listening to what the other person has to say, I find myself concentrating on thoughts like "Wonder if it's alright to stop looking at them now" or "Oh no, am I batting my eyelashes too much?"
Of course there are reasons for behaving like this, but I need to get over them. No idea how, though.