In most cases, you can't sue your employer either during or after filing for workers' compensation.
That's fine in many cases because the advantage of the workers' compensation system is that you don't have to prove that your employer was at fault to win.
However, this means that you can't sue for pain and suffering damages under workers' compensation. To sue for pain and suffering or emotional stress, you have to file a personal injury lawsuit and prove that your employer was at fault.
The bottom line is that most types of workplace injury claims can only be resolved through the workers' comp system, while very few claims can be resolved through a personal injury lawsuit.
If you filed the wrong type of claim with workers' comp, it would be dismissed, and you can probably file a personal injury lawsuit, but only in rare cases will you have the option to choose which system to use to resolve your claim. Consult with your lawyer if you are unsure.