How can I fix my smile that looks like a sneer?

Even with braces, at the end you will have the same teeth ,yellow and same shape, only that they will be straight. you want to have a change? go for a complete smile makeover, you have a high lip smile, a gummy smile,you need a gingivoplasty, and veneers or zirconium crowns.that way you will...

A combination of Orthodontics and veneers will help. Also subtle lip filler can change the way your lip looks when you smile. You can achieve what you are looking for but it will take time and money. Consult an orthodontist as well as a cosmetic dentist. 

Issue is not with gums. gummy smile does not looks good. issue is with buccal corridors [dark areas on both side of teeth]. best option in yr case is expansion of arch. demon braces or aligners are good option for u.