I agree with Richard Heck's response, but would like to respond to the first part of this question. I think there are some fairly persuasive reasons for thinking there is no such thing as eternal life--though I doubt that an argument could be given to show its impossibility. So:
(1) If we agree that the body dies and is ultimately destroyed as an entity, then the only way there could be eternal life would be if the living self is entirely distinct from the body. But the kind of mind-body dualism that might make this possible has been shown (in many ways and by many philosophers) to be at least profoundly problematical, if not simply incoherent. Indeed, many philosophers regard the very idea of "disembodied existence" as problematical, if not simply incoherent.
(2) Even if survival of death means re-embodiment in some form, it would still appear that the living self is entirely separable from the body that dies, so that does not solve the problems of (1). Similarly, there seem to be fairly strong conceptual reasons for supposing that theories of reincarnation or transmigration of consciousness are incoherent. There are many technical reasons for this, but for an intuitive grasp of their gist, consider: Is it really imaginable that you could be both YOU and also A CHICKEN (for example)? How can a being have BOTH a human and a chicken form of consciousness (whatever that might be like)? If "what it is like" to be a chicken is something in principle not available to you, then actually being or becoming a chicken is something that in principle cannot happen to you--either you would not really be a chicken, or else you would be destroyed in the process.
Unless there is some other (coherent) way to conceive of eternal life, then I think you would do well to worry about the one (mortal) one you have. Last chance!