I am abroad, how can I apply for international roaming data?

That depends on whether you are prepaid or postpaid.

If you are a postpaid customer, you should have received a text as soon as you connected to a foreign tower informing you that international day pass would be added to your line. That would allow you to roam in another country for $10 a day on any day you use service.

If you are prepaid, If you connect to Wi-Fi you would be able to receive a text via Wi-Fi.  If you do not have access to Wi-Fi, you would have to be in a country that allows the prepaid roaming add-on.

https://www.att.com/prepaid/static-pages/intl-travel-add-on/

I don't think either case applies to me.  Because I didn't receive a text message after connecting to a foreign tower, nor did I receive a verification code text message after connecting to Wi-Fi.  And I am not currently in the country listed in the link below.

Well for starters you have to be either prepaid or postpaid.  If you could figure out which, that might help you. Prepaid means you refill every 30 days. Postpaid has the billing or autopay on the exact same day every month. Even if the month is short like February or long like December, August, May