Based on the way you have explained your issue, I must assume that you did not, in fact, work while collecting EDD/UI which is, of course, illegal.
It is difficult to prove the negative, i.e. you did not work in the period that you were paid Unemployment Insurance. In order to collect UI, you must be available and able to work. You are also supposed to be looking for work. If you complied with these requirements, you should gather as much information as possible about your efforts to find work. This should include (1) a resume you sent or delivered to prospective employers; (2) a list of names, addresses, phone numbers of employers and the dates you contacted them, whether by mail, phone or in person; (3) responses from any employers you contacted, especially if written; (3) if you used a computer to search, perhaps you can print a computer History of websites visited looking for work ads, job offers, etc; and, of course, witnesses who would have reason to know whether or not you worked in the period you collected.
If you were terminated from a job before applying for and collecting UI, did you receive a written termination letter? If you have found work since you last collected UI, do you have the check stub from your first pay period? It should show date you began and Year to Date earnings which would be the same as your first paycheck. This may help you establish the beginning and ending dates of your period of unemployment.
If you were out-of-state, for whatever reason, including looking for work elsewhere, receipts for transportation or gas, car rental, food, hotels, can document the fact that you could not have been working in California at that time (provided that you were not working for a California employer outside of California).
It would also be helpful if you can find out from EDD what they are relying on to support the claim that you worked while collecting. Once you know this, you will probably be better able to respond.
As for whether or not you need a lawyer, this depends, at least in part, on how much EDD claims you owe. If the claim is for tens of thousands, you might want to have legal counsel. If smaller, you could find yourself spending as much for legal help as the claim is worth. Even with legal help, there is no guaranty of the outcome...you could end up paying a lawyer and paying EDD.
This answer is a general statement of some of the principles and issues applicable. Because I do not have specific details of your situation, I can not make specific recommendations or an accurate analysis of your risks or the potential for a successful outcome. This is not intended as, and you should not take it as, specific legal advice about your case. It could be in your best interests to consult with an attorney of your own choosing to review the details of your matter for more specific advice.