American and Alaska have different record locators when you buy a ticket for an Alaska flight on aa.com, and the American record locator won't work on Alaska for seat selection (it won't work at all for anything, really).

What you need to do is get the ticket number from the receipt (or your name+flight+date) and call Alaska, and with that information get ALASKA's record locator. That will let you pick a seat on alaskaair.com, and should let you check in (since you need to do it with the operating carrier, IIRC).