Dial the American Airlines customer service phone number at +1-866-980-7279 or 1 (800) 433-7300.
When you call the number, you will get a computerized voice that will help you with the steps. You need to follow all the steps and then your call will be transferred to the customer service agent who will help you with your concern.
If you dial the American Airlines phone number +1-866-980-7279 or 1 (800) 433-7300 and due to network issue, you get disconnected, you can use other means given below.
Source: https://www.qxbooking.com/blog/how-to-talk-to-someone-on-american-airlines