If you've sent your application by mail it's a bit tougher as you don't have online access. It might take a while for your application to go thru the central mailing centre. So there is actually no number to follow-up with the application processing.
When I called, i had already confirmed my interview date/time and was inquiring about my spouse application. It's honestly super busy and I had to try calling 5 times to reschedule my Appointment.
I know this reply doesn't help you, but rest assured it's in their system. Once the application is thru- you'll receive your conditional approval and that's when you can register online and choose an interview date/time.
If it helps. We did our interview together, and my spouse got their card 1 week after, and I've yet to get my card..... (2.5 weeks now) and the kicker..... I can't even use it during this upcoming trip
Good luck Toy Story Fan