How much interference is allowed to pass FCC verification testing?
You are likely to be dealing with FCC part 15 rules.   https://en.wikipedia.org/wiki/Title_47_CFR_Part_15 is a good primer.   The idea behind the rules in to ensure that devices you buy don't prevent other devices you own from working with regard to radio.  You will probably be interested in 15.1XX part of the rules found here.  You will want to see if you are exempt for a particular reason, or you will have to try to do a rough calculation of the radio power coming from your device.   The AM radio is a good start, but I am not sure if the distances are good enough.   

I would try to find other products that are in a similar realm to yours and see how they measure up.   If they have similar characteristics, you are probably in good shape ( I am no means an expert).  Something else you could do potentially is get a spectrum analyzer and put a simple antenna on it for an input and see at what frequencies you are offending and maybe have a better idea of from where.   And as always, shielding or a grounded metal case can solve most problems.

As a note, FM will 99.999999% of the time not be effected by this sort of thing.   Both the frequency and modulation type make it fairly immune to the sort of interference caused by things like switching power supplies