Lips often heal this way. You can ask your doctor for a kenalog (steroid) injection. A small amount of steroid (less than 0.1 cc) should soften that area.
Typically problems like yours are related to breathing and tongue position.
Start treatment with an Oral Myofunctional Therapist who can then guide you to an educated airway dentist or orthodontist.
Do not let anyone amputate teeth but you can consider Epigenetic Orthopedics with a DNA Appliance.
The labial frenum is usually at the center of the upper lip. If the fremum has a low attachment it can create at space between the upper two teeth or prevent the closure of a gap with orthodontics. Based on your photos it appears your teeth are off midline to the left. This could be corrected...
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