When should I opt dental braces either before or after the frenulum surgery?

Hello doctor,

I am 19 years old. I have done canine impaction surgery just before two weeks. The stitch and the removal after the surgery have caused a cut on my gums, which now separates the point at which the gums above the central incisors meet. The point that I am mentioning is right below the frenulum. My dentist said I am having class 2 labial frenulum and that it might result in gum recession and the formation of a black triangle.

He added that it might prevent my gums from joining back together. I did not have any bad experiences with my frenulum until the surgery. I am afraid to undergo this surgery. Moreover, I do not want to undergo this frenectomy. All I want is my gums joining back. Please let me know whether I need to undergo this frenectomy. If yes, let me know when would be the right time to do it. I am planning to wear dental braces after two months. Should I do it before or after the surgery? I would be very grateful if you suggest me a way to join my gums back without undergoing frenectomy.