Does my bottom bracket need replacing?
If it's only 2 months old, they have to replace the broken part in guarantee for free. Isn't it?

Anyways I checked the specs, this bike has Truvativ Firex GXP crankset. It has integrated bearing, so it should not move side to side. The clicking noise usually means loose or damaged bottom bracket. First I would try to reinstall the crankset with correct lubrication and optimal torque. And if it does not help, it has to be replaced.