Mold spores tend to gravitate toward places that are moist and have air and organic matter to serve as food. This combination of conditions can be found everywhere from furnishings to cardboard boxes, but as you and your son have unfortunately discovered, one of the biggest and most often overlooked homes for mold is the air conditioner.
Whether a portable or part of a central air setup, an air conditioner's coil and everything around it is damp while the machine runs, which attracts mold. Without adequate filtration, mold is bound to grow.
Using a decent filter can make all the difference─that means a pleated filter with a MERV (Minimum Efficiency Reporting Value) rating of at least 8, or 11 in the home of someone prone to allergies. If the air conditioner in your son's apartment is a wall unit, its original filter would've had a MERV rating far lower than 8, so an immediate filter upgrade is in order.
Considering your son's serious condition though, the best advice would be for him to move out. There's no sense staying there if it is making him sick. Mold effects different people in different ways and if he is that sick, he needs immediate medical attention and a clean, mold-free place to live as soon as possible.