Could damon braces, a dna appliance, or Invisalign correct my problems and give me a broader smile?

You have a primary orthopedic problem and the DNA is the best treatment.  Growing your maxillar wider will allow correction of narrow smile, fill the buccal corridors and help the gummy smile.the DNA /RNA version of the appliance orthopedically grow your bones via epigenetiic orthopedics and also grow your airway which can help headaches, migraines and sleep apnea.There are surgical interventions that can be preformed but are usually are best avoided.There are also Cranial Manipulation techniques that when used in conjunction with Neuromuscular Dentistry can correct the canted maxilla.If you are not having severe headaches I would start with the DNA appliance.  If you have a chronic pain problem start with neuromuscular dentistry. Visit Reddit / DNA Appliance to hear more patient videos

It would be impossible to make specific recommendations with only a description of your problems but I can give you some general information.

A gummy smile is a clear indication that your jaws are underdeveloped. Crowded teeth are also a clear symptom of jaws that are underdeveloped.

By your description, it also sounds like you have a lower jaw that is too far back. This is best fixed by moving the lower jaw forward NOT by retracting the upper jaw. This can be accomplished with a number of appliances, the most well-known being the mRNA. Invisalign can also accomplish moving the jaw forward but is definitely an advanced skill requiring a skilled provider. Damon braces will NOT move your lower jaw forward.

Good luck!

You are a great veneer case but you are very young. Your smile can easily be widened with Lumineers or other no-prep veneers. Your question is how much upkeep do you want to deal with? These can look beautiful but you will need to redo at some point in your life. If this doesn't bother you then move forward with veneers if this bothers you get a second opinion.