In addition to the obligations of landlord contained in your lease, the landlord has certain statutory obligations which are contained here: http://codes.ohio.gov/orc/5321.04. There is a requirement to keep the premises in a fit and habitable condition (see 5321.04(A)(2)). Tenant's remedies for the landlord's failure to comply with those obligations are contained here: http://codes.ohio.gov/orc/5321.07. This section requires the tenant to give the landlord a written notice of any defective condition and request that the landlord remedy that condition. If the landlord does not remedy that condition within a "reasonable" time period, generally thirty days, AND the tenant is current in rent, the tenant may take the various actions described in section 5321.07. Those actions include, but are not limited to, terminating the lease.
So, I would begin by sending your landlord a written notice of the presence of black mold and requesting that the condition be remedied within 30 days pursuant to Ohio Revised Code Section 5321.04 (either deliver the notice by hand or send by certified mail/return receipt so you can prove when the landlord received it). Hopefully upon receipt of that notice the landlord will fix the problem. If not, you have the remedies in Section 5321.07 available to you.
Because this process needs to be done in strict compliance with the law and terminating your lease (or taking the other action permitted by 5321.07) is tricky and can have serious consequences, I would strongly recommend enlisting the assistance of a local landlord/tenant attorney to guide you through this process. I hope this was helpful, and best of luck to you.
I am licensed in the State of Ohio, posting a response to your question or issue does not create an attorney-client relationship and I AM NOT providing you legal advice. You should speak with an attorney who is licensed in your state to whom you have provided all the facts, before you take steps that may impact your legal rights--or rights to recovery of damages.
Ms. Marshall is absolutely correct. In addition, I would go to a Lowes, a Home Depot or other home improvement store and purchase a mold testing kit to determine what mold you are dealing with. They are relatively inexpensive. You should also be aware that statute of limitations on other actions available to you and your family begin to run when you are aware there is black mold in your apartment. It is imperative you contact an attorney who handles landlord & tenant law as soon as possible. Good luck to you.