Short answer is "no." A worker who suffers psychological harm in the course and scope of his employment is entitled to worker's compensation benefits. As a general principle of law, those benefits are his EXCLUSIVE remedy with respect to his employer. The deal with worker's compensation is that all the employee has to prove is that he suffered injury in the course and scope of his employment. He doesn't have to prove the employer's negligent breach of a duty, which is the way it used to be. In exchange, the employer has to pay for the worker's compensation benefits, but gets immunity from suit. Which means, in the ordinary circumstance, employee can't sue employer. (There are some rare statutory exceptions to this rule, applicable to employers who are derelict in their responsibility to provide worker's compensation benefits.)
The worker's compensation bargain represents a big improvement over the previous state of affairs, where even the smallest bit of negligence barred an employee's recovery ("contributory negligence"), where the participation of a co-worker in the circumstances leading to the injury could bar the employee's recovery ("the fellow-servant rule"), and where the employee could be deemed to have assumed the risk that he would be injured ("assumption of the risk"). "Contributory negligence," "assumption of the risk," and "the fellow-servant rule" -- sometimes called "the unholy trio of the common law" -- made it almost impossible for employees to recover from their employers for work-related injuries. But the advent of worker's compensation laws changed all that.
You may be entitled to worker's compensation benefits on account of your PTSD, but to qualify, you will have to establish that your PTSD arose out of your employment with your former employer. That may be a tough row to hoe. On the other hand, you won't be awarded worker's compensation benefits if you don't apply for them. The place to start, I would think, is the worker's compensation division of your state's department of labor. State governments generally employ people whose job it is to speak with injured workers about opening claims for benefits.
Not legal advice as I don't practice law in Alaska. It's just my two cents on the facts you describe in light of general principles of law. Please consult an Alaska worker's compensation lawyer if you need legal advice, not me.