Penalized? It is not a criminal offense. You will have serious issues when and if you decide to renew your visa, apply for change or adjustment of status or anything else in between.
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A few things in your question raise my concern. First off, what relevance is the fact that she was black? Secondly, I don't know what you mean by 'justified infidelity' but it would probably have been better for you to break things off with her before engaging in the 'justified' infidelity - I am sure you would have wanted that respect had you been on the receiving end of such infidelity. Finally, as to your question, it is not a good idea to work without authorization while on an F1 visa. There is a tight exception for emergencies for students to obtain employment authorization, but I am not sure if your situation as described would qualify for this, so you should consult an immigration attorney directly for more guidance. As to if you can work under the internship capacity, I would ask the school's DSO. I would strongly advise you not to do it on your own without authorization.
This advice does not form an attorney-client relationship and is merely informative. It should not by itself be relied upon to address a legal concern.
Why is the fact that she was black relevant in asking your question? In any event, this will certainly come out if and when you try to adjust your status.
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It's unauthorized employment and it will affect your future immigration status.
Due to the nature of this forum, Attorney Maria J. Marty does not have all the information required to provide legal advice. Accordingly, her responses on Avvo are intended as general and not legal advice.