Here are AA's rules for getting on an earlier flight:
https://www.aa.com/i18n/utility/sameDayTravel.jsp
If it's available, it'll cost $75.
If you are hanging out in the airport, look for the DFW Airport Travel Lounge at gates A29, B8, B28, C8, C27, E8. These are free, small areas (~10-20 seats), quiet and out of the way, with cushy seats and desks with outlets. Most are tucked in behind starbucks.
What day of week?