It could cause an infection if it's deep enough. You can continue to try soak it in warm water, also try soaking it in peroxide as well. You can slowly work it off, just don't pull it with force. But if you keep it on, you can risk infection which will interfere with the healing process.
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There is nothing a doctor can actually do for it other than to keep it clean. Stitches can be used because then the skin will become to tight. (if that makes sense) Even if it's deep, during the healing process your body will build new skin layers. You may have a scar there, but it will heal and it may take 2 months (depending on how well you take care of it these first few weeks and how your own body heals) But you need to get that bandage off. The main things to try to soak in is warm water, peroxide is good or Epsom salt warm water. Chances are you will have to pull it some if it's stuck that good. Just be as gently as you can.
When you do get it off, then wash it well with antibacterial soap (making a later with your other hand if you can. Rinse and pay dry. Apply a cream like neosporin (make it a good layer for the next few days and re-wrap with gauze or something over it to protect it. After a few days you will begin to see where your body is making the new skin layer. Once the new skin layer is there, then apply the neosporin and no more covering... and it will heal. It will take some time.. the main thing is to keep it clean..
Hope this helps Hun.