Candidates of Vaginal Rejuvenation or Vaginoplasty surgery are women who desire a more youthful appearance and function of the vulva and vaginal area. For some women, various events result in loss of strength and tone in the vaginal area, although it may be difficult to tell where this small piece of skin came from.
In surgery the lining of the vagina can be reduced, removing excess and redundant mucosa decreasing the diameter of the canal. The muscle ring, pubococcygeus, at the entrance or introitus can be tightened. These procedures along with exercises such as Kegles can help keep the muscle tone in this area. Aesthetic Vaginoplasty, in many cases, can increase friction during intercourse, giving women more control of vaginal muscles, increasing sexual satisfaction, while also creating a more attractive and appealing appearance to the vaginal area.
It sounds like you may still have an unbroken section of your hymen. This can be corrected by your gynaecologist.
This is a hymenal remnant most likely that is a normal part of the hymen that has not fully separated. If it causes pain it is worth a visit to a GYN or plastic surgeon to have an evaluation. Sometimes this may need to be released with a small incision under local anesthesia, but everything you're describing is normal and may go away on its own.
The skin flap you are referring to may also be called the Hymen and is normal unless it interfers with sexual intercourse or sometimes even the ability to menstruate. The fact that it is causing you pain and discomfort, the skin flap may need to be either removed or released. You should consult with you gynecologist.
a skin flap is normal, but "pain with sex" means it may need to be adjusted with a small lengthening/widening incision in office. Beware though that scar tissue can make pain still present.