Will my lips and the area above my top lip eventually go back to normal, or will the skin be stretched and be saggy? (Photo)

This can easily be reversed with an enzyme called hyaluronidase, and no HA injections on the lips leave permanent long term changes.  Cannulas limit complications. Best, Dr. Emer.

I'm sorry you didn't get the results you were hoping for. It would be helpful to know when the injections were done, what product was used and what volume was injected. You don't need to worry about the filler leaving your skin stretched out and saggy. This was a concern early in the history of fillers and was researched. If anything, your skin will be more elastic and firm after the filler wears off. I don't perform a patch test with hyaluronidase and wonder if you are truly allergic. I suggest you see a board certified dermatologist or plastic surgeon who understands and has experience with fillers and the use of hyaluronidase. 

It would have been helpful to know when you were injected.  Don't worry too much about the 'stretched and saggy' skin.  Your lips will go back to normal once the HA filler is gone.  If you are unhappy with the look, you can try hyaluronidase to remove the HA filler.  My suggestion, give it a bit of time...you may love it.