As @ucbalumnus explained, having to get into specific engineering majors once there is the normal program. And I don’t think it will be a problem for you, particularly since I agree that IE probably isn’t one of the highest-demand engineering majors. It’s just good to know what to expect and understand that it’s not direct-admit to the major.
As for EDing to Northwestern, sure, they can’t force you to attend if the financial aid isn’t sufficient. But the usual basis for an appeal is either 1) you can document the NPC results you received before applying, and the actual financial aid offer is worse than that for some reason or 2) your family has had a change in financial circumstances that isn’t captured by the standard financial aid formula. If your situation is 3) “My NPC results never showed sufficient aid, and there are no special circumstances or changes-in-circumstances; I’m just hoping for a miracle”… their reaction is going to be that you shouldn’t have applied ED in the first place.
The good news is that TAMU Engineering has an EA cycle:
So, you should be able to get an answer from them before the holidays. Hopefully you’ll get in and not have to worry, after that, about any place that you wouldn’t choose over A&M.