Having an anxious child can be difficult for a parent. It's our job to help our children to become strong and independent. How can we accomplish this if we don't push them past their anxious moments? There is definitely time as a parent to listen to your child and realize that your "plan" for them may need to be altered.
Here is a helpful guide to distinguish the level of anxiety your child may be experiencing and some tools to implement:
Typical Anxiety: This may be caused by stress or general worry over an upcoming event. This type of anxiety doesn't last long. What can help: exercise/healthy diet, limit caffeine/sugars, adequate sleep, soothing music, conscious breathing/yoga, deep pressure therapy.
Generalized Anxiety Disorder: This is determined by a professional through evaluation and assessments. Signs and symptoms associated with generalized anxiety includes: persistent, excessive and unrealistic worry about activities of daily living. Inability to relax and sleepless nights. Fatigue, nausea, racing heart are also common. What can help: counseling/therapy and prescribed medication, in addition to what is listed for "typical anxiety". Weighted anxiety blankets have been known to help with generalized anxiety and helping to achieve a more restful night's sleep. Natural sleep supplements are also a good idea. I have used Melatonin and seen great results in my children's ability to fall asleep faster. 
Severe Anxiety Disorder: All symptoms are amplified....severe panic attacks, shortness of breath, chest pain, sweating, palpitations, numbness, intense fear, flashbacks and feeling that you are crazy. What can help: in addition to tools listed above, it's important to seek professional help. It may be suggested to take prescription medication/SSRI's, counseling and various therapies. It's important to find a professional that you and your child are comfortable with. Research the different type of therapies (Cognitive-behavioral, EMDR, exposure/response) to determine what will be best. Then seek professionals that specialize in that particular therapy.