I don't really think Voldemort was self-conscious about his looks, if that's what you're asking. I think when he was younger, he knew that he could use his charms and good-looks to his advantage, and they were moderately important in that way. I don't think he was vain superficially in that way, because he did not love, and did not need anyone to accept him for the way he looked. Voldemort's sole thirst was for power, and I don't think something as shallow as the way he looked would have gotten in his way. At Hogwarts, however, I imagine him using his handsomeness to manipulate the teachers and students since he had no real "power" over them.
But once he got his Horcruxes, he did not need his looks to help empower him in any way--in his mind, he already had all the power he needed. Looks were not important--he was nearly about to rule an empire! I don't think he cared how different he appeared, to be honest. He might have even relished in the fact that it made more people fear him.
Hope this helps
xx Ariana xx
Edit: This is in response to Lovemagic's post!