Yes, it often hurts to look directly at someone's eyes, although I can do it intermittently to the degree that most people don't seem to notice that I avoid it. The psychologist who evaluated me for ASD noted it though.
It also often hurts to speak.
I also look at people's mouths when they're speaking, and find it pretty difficult to look away, but I've learned that when you do that in person it often makes the other person uncomfortable, or even angry and agressive, so I'm more likely to do that when the speaking person is recorded (like on television), or if they don't know that I'm doing it (like if they're on stage, or speaking while looking at someone else in the room). While looking at a speaking person's mouth does make it easier for me to focus on, and comprehend what they're saying, I think the difficulty in looking away is associated with a feeling of dread. It feels unsafe to look away.
If I'm having a one on one conversation I try to make eye contact occasionally, but a lot of times, that's for the benefit of the other person, to reassure them, since it seems important to them. It doesn't benefit me generally, and makes me anxious, and even nauseous. For the most part, I look around the room, and find that I can make less eye contact with people if I acknowledge that I hear them by nodding my head, or mumbling, "mmhmm" frequently.
Personally, I think that making eye contact and showing the teeth are threatening behaviors among primates, and it seems strange, and maybe even unhealthy, for professionals working in the field of behavioral health to force humans who feel uncomfortable with those behaviors to perform them.
But I'm not a doctor.