In nearly every case, yes, you need your own attorney. The EEOC is not your representative. A mediator for the Equal Employment Opportunity Commission (EEOC) has one client - the United States of America. Some EEOC mediators are great and will do their best to protect you rights even though they are not your advocate. Some EEOC mediators stink and care more about closing the case than they than they care about your rights.
Because the EEOC has a particular mission and because it is not representing you, if it turns out your interests and those of the EEOC clash, the EEOC mediator will first and foremost make sure the agency's goals are carried out, not yours.
Also, the EEOC will only consider issues relevant to laws the EEOC enforces, such as discrimination laws. It will not consider such things as employer liability under state law (which in some states, like California, is substantially more than under federal law), wage and hour violations, mutuality in the settlement agreement, circumstances under which you might have to return the money, the language of the settlement agreement (which could have all kinds of "gotchas" that the EEOC doesn't notice or doesn't deal with), and more.
In addition, EEOC mediators most often handle low-value cases because that is what ends up in their offices. They handle high-value cases far less frequently, and even less frequently handle high-value cases where the charging party doesn't have an attorney. If you show up without an attorney, the mediator may interpret your case as low-value, even if it isn't. Of course the mediator may learn the value of your case during the mediation, but why start off with such a large obstacle?
Similarly, without an attorney, the employer probably won't take you or your case seriously, and may be able to take advantage of you. No one is watching your back if you don't have your own attorney.
Consider that the employer most likely has an attorney or has consulted with its attorney. Even if the employer doesn't have an attorney, it usually has human resources personnel who have been down this route before and know far better than you do how to use the system to its own advantage.
It is nearly always the case that a charging party will do better overall with an attorney, even taking into consideration the attorney's fees portion of the recovery.
Employment law is complicated and fact specific. You may wish to speak with an experienced plaintiffs employment attorney.
To find a plaintiffs employment attorney in California, please go to the web site of the California Employment Lawyers Association (CELA). CELA is the largest and most influential bar association in the state for attorneys who represent working people. The web site is www.cela.org, and you can search for attorneys by location and practice area.
To find a plaintiffs employment attorney in your area, please go to the web site of the National Employment Lawyers Association (NELA). NELA is the largest and most influential bar association in the country for attorneys who represent working people. The web site is www.nela.org, and you can search for attorneys by location and practice area.
Also, NELA has affiliates in every state and in many cities. On the NELA web site, you can look at the list of affiliates. Some attorneys will be listed in the affiliate membership list, some in the national organization membership list, and some in both. Being listed in one or both lists should not influence your selection because attorneys can choose whether or not to purchase the listing in the national directory. Each local affiliate has its own rules for listing.