Damon made Elena forget that he came into town, therefore made her forget that she met him first. Was it real? or did Alaric's alter ego put it in Damon's head to torture him?

No it had really happened... Damon had made Elena forget it and then earlier when she had been talking to him and had picked Stefan, Elena had said "... maybe if we had met first." After Damon had gotten off the phone with Elena, he had kind of given up, and just let Alaric beat him up pretty much. But then he remembered when he had first met Elena, and I guess the memory of it made him realize that he still needed to fight. But yeah it had really happened it :)

Yes, it was real, because if you remember, Alaric had already died when Damon rushed to the hospital to see where Elena was. That's when Meredith told him that she had 'helped' Elena por giving her vampire blood for her cerebral hemorrhage. Damon, shocked, remembers the memory he took from her the night they met and he called her Katherine--right before Elena's parents turned up to pick her up from the party. After they picked her up, the accident on Wickery Bridge happened and Elena 'met' Stefan.