Hi Ruth,
The key to what your daughter is going through is the feeling of being evaluated - it doesn't matter if it is good or bad. Even though saying "you're so precious" is a lovely compliment, for an individual that is sensitive to evaluation and having focus on them, it can be quite uncomfortable. They often are already so self-focused on their qualities that an increase in that focus from someone external can be unbearable.
So what I am trying to say, is that by increasing her self-focus through the use of comments about her, it only further presses on her "social anxiety" - which is more a fear of people looking at her and having evaluative thoughts of her. If you want things to go more smoothly and support her, shift the comments away from intangible qualities (e.g., preciousness) to things she has control over. Focusing on intangible qualities which seem to change depending on who she is around (e.g., peers or parents) can be quite distressing when you are a teen. Instead highlight to her when she has done a good job, that is, a focus on behaviours.
Also remember that it is important for teens to figure some things out themselves. To become upset and then to learn how to self-soothe - a very important skill to have developed by the time she reaches adulthood.
Don't let your own anxiety be a driving force in her anxiety. Model to her behaviours that demonstrate coping with anxiety. E.G., by verbally saying "Hmm I'm feeling nervous about a meeting at work today, but you know what, I'm just going to dive on in and give it a shot".
I hope some of this was helpful.
