What is the reason for a girl feeling distress and pain in her chest and heart, along with a headache, when hearing or reciting the Qur’an, and how can this problem be treated?

Satan may delude you with that to deter you from remembering Allah and listening to the Quran, or perhaps you are afflicted with an illness like magic. Continue listening to the Quran and strive against yourself until the pains disappear. Recite permissible ruqyah upon yourself, such as Al-Fatiha and the Mu'awwidhat (Surahs Al-Falaq and An-Nas), and diligently supplicate to Allah the Almighty to remove what you are experiencing.