This may not be something that you want to hear, but I was once where you were. My circumstances were not quite the same, but I had the anxiety and a constant fear of death, as well as an inability to stop thinking about it. So here is my input.
In many spiritual traditions throughout the world, contemplation of death is a fundamental part of practice. Hindu yogis often meditate in graveyards, and it was a common Buddhist practice to have a human skull on your desk. The reason is that deep contemplation on the subject of death has the ability to lead a person to a state where one is open to the ever-changing reality around us, and to deeper spiritual understanding.
You were faced with a situation where you truly thought you were dying. Your Ego was forced to confront its own destruction, and it is having trouble coping with such a fact. This inability of your Ego to cope with death is what is fueling your anxiety. So my advice is this... continue thinking about death. The issue is not that you are thinking about death (contemplation of death is a fundamental part of the spiritual path in my opinion). The issue is that you fear death. Distracting yourself will not help, as you will always have that fear in the back of your mind now. You cannot simply forget about it. Death is not something that you can escape. In order to progress, you must confront your fear. You must face your notions of death, and see it for what it truly is.