+1.800-843-6200 works in the USA, of course, but I am unaware of a toll-free available in Thailand. EXP guide merely states:
Outside of the continental U.S., Canada, Puerto Rico,
Guam, Saipan or the U.S. Virgin Islands, contact your local American Airlines reservations office. Or you can access the U.S.-based service desk from many global locations. For detailed dialing instructions, visit usa.att.com/traveler (long distance charges apply)
(I use Skype from my smart phone using WiFi or from a computer.)