People often believe that government workers would receive more favorable treatment than private sector workers but in my experience the opposite is true. You would be well advised to obtain representation because federal eeo law is a trap for the unwary. All the eeo people who are supposed to be there to help you, etc., may not be. You should find a lawyer who specializes in helping federal employees. Good luck to you.
It sounds like you admitted to a violation of a work rule (by making your written apology). If so, your employer may have rights to terminate you unless you have federal civil service protections, work rule formal policy protections, or an employment contract.
You weren't fired on grounds of discrimination. You may contend that your termination was unlawfully discriminatory, but it is important for legal analysis to identify the employer's stated ground for your termination. It is also important to know how long you had worked there. Were you covered by civil service? Were you still on probation? Was the infraction that you admitted caused by the disability that was identified at the time you were hired?
You do not need to answer these questions here, but these are the critical details. Consult with a local attorney with specific experience in federal employment for further analysis of your rights and options.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.