Generally corporations must be represented by counsel when they sue or are sued and advancing a defense.I do not know the details of your engagement contract so you should, at minimum ,seek the advice of an attorney to read the document for you and explain to you what your rights are. I wish you the best.
Under some circumstances, a Florida corporation, including an LLC, does not have to have an attorney represent the corporation in Small Claims court. The collection of Florida Rules of Civil Procedure apply to all Florida court actions, including Small Claims Court. For Small Claims Court however, there are an additional set of Florida Small Claims Rules which apply only to that level of court. If you are going to continue representing your corporation in this proceeding, you should find a set of these rules at your local law library and get a copy.
Most important to you is Small Claims Rule 7.050 "Commencement of Action; Statement of Claim" That is the rule which allows most corporations to sign their own statement of claim. Later in that rule it states: "A corporation may be represented at any stage of the trial court proceedings by an officer of the corporation or any employee authorized in writing by an officer of the corporation." So if you are an officer of the corporation, you are fine and have full authority. The rules also have a forms section, which includes a form for a corporate officer to give an employee written authority to represent the corporation in Small Claims Court. Although you CAN do it, if the other side is represented by an attorney, you should strongly consider whether you should engage an attorney also.
Your opponent was quoting or referring to another Small Claims Rule, 7.090(f) "Appearance at Mediation" This rule suggests an attorney may appear at mediation alone, without the client, or a non-lawyer representative may appear with written authorization. No part of this rule cancels or trumps the first rule quoted above. If you are a corporate officer, you can still appear at mediation and do everything by yourself without a lawyer.