I asked my mom for you Ashoor, since she is a hygienist. Since you say you floss on a daily basis, here are her thoughts:
1. You floss incorrectly. You have to glide the floss gently and as close as you can to the tooth so you dont cut into the gums.
2. You floss to fast. Flossing quickly to get it done will not be correctly done, you wont get deep in between the tooth and gum, so you will start to bleed again like you did when you first began to floss. Also, flossing quickly is an almost sure way to cut into your gums.
3. You brush too hard. Brushing can push your gumline back, so when you begin to floss you are flossing in between teeth and gums that have never been exposed to floss before, which is quite painful and creates more of a recession with your gums.
She said try to get your dentist to give you soft-bristle tooth brushes. Not the ones from Oral-B or anything, they are pastel color brushes with VERY soft bristles. See if you can get a bottle of Periodex mouth rinse as well, that will help "cure" any of the rough spots between your gums.