Is what I am doing correct by drinking Zamzam water for healing after reciting Al-Fatiha, Al-Ikhlas, Al-Mu'awwidhatayn, and supplicating three times? And is there another method for that, specifically regarding ruqyah sharia?

Zamzam water is blessed, and in it there is healing and sustenance. Its goodness increases if it is drunk with the intention of healing and if the Qur'an is recited over it, especially during the time of sahar (the pre-dawn hours). Supplicating when drinking it is commendable, and there is no specific supplication authentically reported from the Prophet, peace and blessings be upon him. However, it was narrated that Ibn Abbas used to supplicate: "O Allah, I ask You for beneficial knowledge, abundant provision, and healing from every disease."