Our daughter cut her forehead quite badly when she was 17 months (fell over on a pavement). She was treated the same way in a&e with the strips and told it will heal. I was really worried as the cuts were large and right there in the middle of her forehead. It took a long tone to heal and she was left with a large red marks. I was really worried and even got her fringe cut so it will cover it . Fortunately they disappeared after just over a year.
She is 5 now and I can't even tell where she had the cut.
So don't worry. It will take a while but should heal completely.