Unless things have changed a lot in the past couple of years (which they might have), I wouldn't want much less than 3 hours even with checked-through baggage. Make sure AA & Aer Lingus can interline your baggage. Otherwise I'd go for 4 hours. Sounds crazy, I know. Then again, this is based on the last time I had to to do T1-T3 shuffle (the reverse of what you're doing) and the three hours between flights, even with checked through baggage, didn't leave much extra time. If I recall correctly I had to go through security twice, and one of those two times had the worse security line I've ever been in (crowded hot room with huge lines).

I've got another T1 to T3 flight coming up in a couple of weeks, and I've allowed four hours, even with checked-through luggage. What, me, paranoid?