No, you can't sue your employer or co-worker for causing your injury or illness. You can only file for workers' compensation to pay for your lost wages and medical bills. You are not paid for pain and suffering from your work injury.
There are two exceptions:
If your injury or illness was caused by a defective product, you may have a personal injury case against the manufacturer of the product.
If a co-worker assaults you based on a personal matter; you may be able to file a civil or criminal lawsuit against your co-worker.