I'd think if you do you may have to move while they remove it. If you are indeed getting sick from it then I'd consider moving anyway. I suppose your apartment manager would have to pay for your living expenses while you were relocated while they clean it up but maybe not. Consider all options.
You should contact your apartment manager ASAP. Mold can cause serious health problems. When there are children involved, it is imperative to get this taken care of right away. Your apartment manager has an obligation to fix the problem. If you have to move out of the apartment, you should be compensated in some way. If the manager doesn't take care of the problem, call the local health department. They will send someone over to investigate the situation.