Yep, if you know the correct USA number to call, here's the FAQ on Skype for that circumstance:
https://support.skype.com/en/faq/FA2...-number-series
I haven't had to redeposit miles yet on AA but, on UA, when I did, the miles were back in my account in minutes. I imagine AA is similar. The taxes usually refunded within a few days, a week at most.
Be calm. They'll fix you up.