If it's just a lack of confidence it sounds like she needs a confident handler to help her overcome this. I would separate her from the other horse to encourage her to look to her human for confirmation, not to the other horse.
Take her to a round pen or an empty field, I wouldn't honestly round pen this horse, it sounds like if you chase her you'll just scare her. So Take her in on lead and practice her letting you touch her all over. Rub your hands up and down her body, in a pleasant sort of rub, not tickling like bugs and not invigorating or rough. Start somewhere she likes and move around, work in each area until she's completely comfortable, if she becomes very uncomfortable move back to where she was and ease your way back to where she wasn't. Work on this until you can touch her Everywhere.
Then practice basic ground work, yielding in all directions, backing, yielding front end and hind end. Leading her around, build her confidence in people. Give her a reason to trust people, not depending on another horse.