why does he see it burned in the mirror?

It looks like Adam's blood cured him totally (and his whole face was burned, not just one side) yet "later" we see nathan looking at himself in a mirror and seeing half his face burned. Also, at that point we thought he was feeling bad about Peter's death, but now we know that Peter saved him and brought him to the hospital, (he knew that, right?)
so what's his deal?

It was all psychological as made clear when the "Nightmare Man" had Nathan fighting his burnt self. It was all guilt over Peter's death. Nathan was unconcious the whole time so he obviously didn't know that Peter was the one who saved him.

Nathan was pretty badly injured after the nuke, and was knocked unconcious after the blast hit him. As a result, he has no recolection of Peter taking him to the Hospital. As for the flash backs, i can only describe them as "bad dreams" or maybe like a bad smell which sticks with you. After all, he did look at himself in the mirror!

and plus it was probably a director's thing too, just to get the viewers intrigued

...or maybe something to do with a 'suggestion' that Angela made to him - to make sure he never forgets what his brother did for him? I dunno I'm guessing , but Angela's ability is becoming very clear now after the thing with Nathan's wife.

Him seeing his burnt face I think was more his guilt over Peter "dying" then anything else. Like he feels that if he decided to side with Peter sooner he wouldnt be dead.