You should assume that the company will have a lawyer present at the mediation and it's always a good idea to have your own representation.
It is not necessary to be represented at this level of the grievance process, but I think having an attorney shows strength and determination on your part and may facilitate negotiations.
I presume that you filed a complaint with the SC Human Affairs Commission and they are the ones responsible for setting up the mediation with the employer.
Simply because the ESC ruled that you were entitled to unemployment compensation, does not guarantee you will prevail in an EEOC mediation. The ESC determination is not binding in any way and does not constitute a prior favorable determination wherein you can rely on the doctrine of res judicata because the issues are different in each tribunal.
The SHAC/EEOC representative is not your advocate at the mediation and I can guarantee you that your employer will be legally represented by competent legal counsel. It is not mandatory that you have legal counsel at the mediation, however, it is very risky to proceed without competent legal representation at the mediation,
My comments are not intended to establish an attorney-client relationship, are not confidential, and are not intended to constitute legal advice. Proper legal advice can only be given by an attorney who agrees to represent you, who reviews the facts of your specific case, who does not have a conflict of interest preventing the representation, and who is licensed to practice in the appropriate jurisdiction where the legal issue may be filed, and who is licensed as an attorney in the state where the law applies.