You may absolutely sue a third party – that is someone, other than your employer, who negligently, recklessly, or willfully injured you.
The catch to this is that your employer may also sue the third party in an effort to recoup the money that has been paid out on your worker’s compensation claim. There are very technical laws regarding who gets first chance at this and how the money is distributed. These are more technical than can be explained here as they are quite detailed.
Generally, your workers’ compensation claim will be handled first and possibly resolved prior to the personal injury claim being file or at least resolved. While it isn’t required to use the same law firm for both claims it is often helpful to do so. Additionally, it is generally best for the attorneys handling your personal injury claim to be involved at least partially in your workers’ compensation settlement. There are certain ways of settling the workers’ compensation claim that will give you more money in your personal injury case.