not actually, when he asked harry to look at him, he just wanted to see harry's eyes which was said to same as his mother i.e. Lily, the person who snaped loved, last reminder of 1st and last love, only light and regret in his life. He wanted to see only living proof of his love - lily. Though true, in movies they didn't show many things regarding draco malfoy but considering the fact they didn't show it all, it would have been weird to suddenly show his character development without actually explaining its background or how it reached that point. That's why the deleted scene on movie 8 was deleted where draco threw a wand towards harry during battle of Hogwarts.
Snape, a total gray character, whatever he did was for his selfish reasons only. he became the same what he hated, probably worse than that. A bully to kids when their age was less than his total career(16 years). He loved lily in his own way though.