Welcome & sorry to hear about the brake/battery problems. You are right, it COULD be the BCM (body control module) draining power from the battery. It could also be an alternator not charging the battery properly. But, chances are that it IS the battery, as it may be 3 or more years old already. If you bought it from a dealer, you may be able to get coverage for it. Sure nothing's left plugged in & on?
You can check the battery voltage across the terminals with a voltmeter, or get an approximate idea with a voltage checker that can be plugged into an accessory outlet. You are looking for 12.5V or better with engine/car completely turned off (no key in ignition etc), and 13.5V or more (ideally in 14+ range) with engine running and all accessories off (no AC, no stereo, nothing in the power ports, etc). Videos on youtube will help if you have never used a VM before, or this will.
Did you have to pay for the brake booster? What was wrong with it?