It may be too late to undo the settlement which you signed and allowed to be submitted to the WC Judge for approval, not to mention receiving the money. Of course, you can sue your work comp attorney but this is a difficult case to prove negligence or malpractice as your lawyer will no doubt argue that your "falsification of a document" may have constituted what is known as the "fraud" defense which means that if you lie as to any part of your work comp claim, you may get thrown out of court without a right to anything. So, your lawyer will argue that he was lucky and skilled to get you $3,000.00. There is also a defense in Florida known as the Martin v Carpenter defense which means that you did not disclose a prior back condition to your employer which is the same as lying on your job application. If this is proven to be true, and if the same part of your back is involved in this injury, your case may again be thrown out of court based on this Martin v Carpenter doctrine in Florida. My advice is to get good advice in person from a board certified WC lawyer in a large city, who represents injured workers, such as Tampa, Miami, Jacksonville, etc. It may not be too late to file another claim against your employer based on a different date of accident then the case you recently settled.
Workers' comp claimants never HAVE to settle their cases, despite what any attorney or assistant might say. There might, however, be times when, despite what the claimant wants or what s/he thinks is fair, settlement might be his/her best option. If the carrier had one or more defenses that your attorney felt might result in a loss of all benefits to you (or, in the case of a fraud defense, possible criminal charges), the attorney might have pushed you settle for what s/he thought was in your best interests. On the other hand, the attorney might run a high-volume practice and might not have wanted to spend the time that it takes sometimes to overcome the carrier's defenses. There's no way to tell from what you posted. So, you might consider talking to an attorney about whether you signed the settlement agreement under duress (which could be grounds to vacate a settlement agreement) and whether your case had more value than you were advised. Also, with all due respect to your doctors, their comments on what you "deserved" are not worth much unless they are also practicing comp attorneys. Comp works differently than other areas of law, and it is often contrary to common sense or logic.