I suffered from anxiety in 2nd grade, and I had stomach aches which was psychosomatic. My mom would give me antacids and I was even taken to the doctor to get checked out. Everything was fine. As I grew up, that all went away. I became more confident and less "afraid" or less anxious. I believe that everyone has anxiety but the levels when you get older are not as high as when you were 8 years old. Therefore, I believe that one can outgrow this type of anxiety and while it doesn't all go away, it can diminish in time.
But now, my son, who is 8 suffers from this type of anxiety as well and am trying to find ways to be able to help him.
Self-help books are one of my go-to solutions, and they have plenty of advice that might help. I find Amazon books to be convenient and if you have Kindle, it's much easier to just download the books that way.
example of a self-help book: Helping Your Anxious Child: A Step-by-Step Guide for Parents by Rapee, Ronald, Wignall, Ann, Spence, Susan and Lyneham, Heidi (Dec 3, 2008)
Your daughter is suffering from anxiety - I suspect GAD (generalized anxiety disorder). This disorder tends to "rear its ugly head" around the eighth birthday - which seems to co-incide with your daughter's age. If anxiety is the issue, I suspect your daughter will not be able to manage her fears without professional help. She will not know "why" she feels this way as anxiety is usually an inherited trait and not the result of life experience.
I might suggest you contact your family doctor; if he/she is unable to help you, then ask for a referral to a medical mental health specialist with experience in anxiety disorders. Treatment does not need to include medication so do not let this prospect prevent you from seeking help. There should be lots of reading on the internet re this issue - "anxiety and school" or "GAD and children" or "anxiety behaviors in children" or similar words/phrases. By the way, if anxiety is the issue (and I suspect strongly it is), then your daughter will not outgrow it nor will it go away but - anxiety is highly treatable, especially in children. I wish you the best ....