M.C.
I'm no expert - my daughter hasn't reached 3rd grade yet, but maybe she is shy and insecure. She has been thru a lot of change recently and stress comes out in various ways with kids. This new school maybe tougher than she is used to, or maybe just being the new kid has her nervous. Sounds like she is afraid of making mistakes. Explain to her nobody likes to make mistakes, but they present a great opportunity to learn.
I agree with with trying to find a tutor. Even is she catches up, she may feel a bit more secure knowing that she has thoroughly covered the material and has a good grasp on the work. If the teacher calls on her, she will be prepared, answer the question, and gain more self confidence.
I'd also suggest giving her nudge socially. Have her invite a couple of friends over to play or for an outing. I think once she feels more settled and secure she will like school more.
Good luck!