Technically, yes, there is nothing preventing you from bringing a workers’ compensation claim as well as a personal injury claim. Of course, these cases will almost certainly involve different parties, because a personal injury claim cannot be brought against an employer in most situations.
However, if you succeed in bringing both cases, you may need to pay back some of the workers’ compensation benefits out of your personal injury case proceeds. This determination depends on state law, so be sure to check with your local construction accident attorney before choosing a course of action.