Do I need to use BX wire in my house?
If you went to a Home Depot very close to your house (in the same town) and they said that BX is required, I would take that seriously and research the finer points of that rule.  A lot of the workers at home stores are not experts by any stretch, but they know what sells and what they have to stock, so there will be some truth to what they "know".

That said, your question illustrates perfectly why location is important, although I totally understand not wanting to give out more info that is needed.  After a little research into Chicago, it looks like you would have to tell us your exact location in order to weed through the various versions of codes that suburbs have adopted, and at that level of detail, a question is considered off topic because it's not likely to be helpful to anyone else.

It seems that Chicago is one of the places that requires metal conduit for residential wiring.  From what I can tell, the city is very strict on it and as you move into the suburbs, they are various levels of strict to the point of allowing NM cable in some areas.

A term that comes up in code discussions is Authority Having Jurisdiction (AHJ).  It's important that you know what jurisdiction you are in so you can ask the right people about the codes in your area.  The county code compliance office should be able to tell you quickly what is required and if you need a permit or if you're even allowed to do the work (in some cases a pro has to do the job).