You have short hair because it looks great on you and it’s your style, so stay true to that for prom. So go as is and rock one of the cute prom hairstyles for short hair!
Prom is fast approaching so it’s not the best time to try out a dramatically different hairstyle. Instead, get a trim a week or two before the big event so hair is just the perfect length.
If hair is dry, prone to frizz, or you just want extra shine, do a deep conditioning treatment at home. The best product out there is Kerastase Nutritive Masquintense and it will last forever with short hair.