In your case, may be incompetent lip means short lip or vertical height of maxilla/ upper jaw is more in compare of lip. It will diagnosed after thorough examination of your dental and skeletal records by various diagnostic aid.
In advanced maxilla various orthognathic surgery required for shortening of maxilla. But it will decided after diagnosis. Now if required orthodontic correction than various other methods like lingual braces, invisalign or clear path.
Next Steps
so please consult an orthodontist.