The school is there only part of the day and part of the year and has a small playground and has restrictions on parents arriving by car, so restrictions on noise are in place, they could argue. I am sorry you are sensitive to the noise but I do not think that it would be strong grounds for a transfer. Techniques like mindfulness can really help with not reacting to noise, etc. It works with lots of people, even with planes, etc. Also, your GP may be able to help with techniques to stop you from getting too anxious about the noise, etc.