I'm not at all keen on this idea that specific symbols in dreams correspond to fixed meanings. The mind is a good deal more complicated than that. Symbols mean different things to different people and trying to formulate a universal dream dictionary where they all mean the same thing too each person is too confined an approach to explaining what dreams actually are. Take spiders for example - to one person they might represent a fear or the concept of intrusion in the home - to me as a tarantula owner they are more likely to symbolise my mothering instinct. The ability to understand your dreams lies not in looking up other people's ideas in books but in looking inward and working out what significance those dream elements have to you as an individual.
Dreams usually do have a significance but their role is more as a filing system for the clutter of the mind. Things that perhaps we need to understand, think more about and focus on often do crop up in our dreams and by listening to the messages in our dreams and looking for the patterns thrown up by our sleeping unconscious minds we can make more informed decisions in our daily lives. Thus the primary role of dreams is to illuminate the present. This is not to say that dreams never foretell the future, precognitive dreams do certainly do occur for some people but they are significantly less common than the dreams that aid us to understand the present.
In answer to your question is your dream a premonition of your own death..? Well yes it well might be. Because if there is one thing we can all comfortably predict it is the fact that we are going to die. It's a daunting thought and one that becomes all the more daunting the closer we get to it. Dreams may well be our mind's way of preparing us -not for near death but for eventual death, a gradual way of accustoming our minds to the fact that one day we will die. Dreams give us a perspective on death and particularly for those who fear exploring the idea of death with the conscious mind the dream world can help accustom a person to face the idea of death. But it doesn't mean you will die soon - you may live another seventy years and live to have many of these dreams preparing you for your eventual and inevitable end.
This article from the Huffington post is worth a read too.