Since my kid is the same, probably worse, I can say that they may not grow out of it. Depends of the reason they are so picky. Does she have sensory issues (clothes fitting weird, sensitive smeller/taster)? Mine son does, along with anxiety about trying new foods.
If sensory is the issue, you may want to get help from an OT. Otherwise, from what I have learned in feeding therapy, is to let her play with new foods. Work on touching them, then putting them near the mouth, then on the lips, then in the mouth (spitting out if necessary), then taking baby bites, then hopefully swallowing.
It may be a control issue, she may grow out of it, she may not. And to those that say 'just don't make them anything else' or make them try it. Have you ever had a kid starve themselves or have a true panic attack when trying new foods?
My advice at this age, always have something else on her plate and let her explore that food (as above). Have fun with it. You can play with your food too! Have her help grow food, go the grocery store with you and make food. All of these will help her get exposure to other foods even if she will not eat it right now.
Good luck!