Burnt skin after Alexandrite laser hair reduction. Do I have to worry about discoloration?

I had my second laser hair reduction session. The first time was painful but my skin didn't hurt at all afterwards. They had used a white pen to mark the area. But the second time I went my dermatologist used a black pen. I was already wondering if that might be a problem but I thought a dermatologist certainly knows better than me. My skin got burnt where the black pen was. I have red strips on my skin now and on one area my skin peeled off, so you see the pink skin beneath it and it's weeping.