I had fractional laser last month on my face, will the grid marks + redness associated with a brown discolouration ever fade?

A week after my laser, my skin inflamed and my doctor advised an oral anti-inflammatory medication and a topical corticosteroid. The first day I applied the corticosteroid every 2 hours, and for a week later I applied it twice a day till the redness reduced and I stopped. Now it's been a month, the redness + brown discolouration are still there, and she advised me to put a whitening cream. She's also accusing my exposure to the laptop for my 'prolonged erythema', though I always apply sunscreen.