Tricky question, but I'm inclined to say no. If you were your sister, what would have happened to her? I think she and you would have to be the same person. But I don't think two people could have been one person. (It's not like Clark Kent and Superman. That is one person in a situation where it is wrongly thought (by Lois Lane, anyway) that there are two people.)

We naturally think of the world as made up of things with properties. Take my black pen: the pen is the thing and being black is the property. But metaphysicians disagree about whether at the end of the day there are things entirely distinct from properties. Some say you need some kind of substance to have properties; others say that a pen is really just bundles of properties: its colour, weight, shape, composition, etc. It's the same with our mental life. I have a headache: "I" is the thing, and having a headache is its property. But some philosophers would say that although we distinguish between the thought and the thinker, at the end of the day the "I" -- the thinker -- is really just a bundle of thoughts. (Insofar as it exists at all.) In that case, I suppose that the "I" would be located in the same place as those thoughts. Other philosophers may wish to insist however that the "I" must be distinct from the thoughts it has: it must be some kind of substance. It might be a physical...

What makes you the same person over time may not be that there is some essence that you have at each time, but rather that your different 'slices' are related to each other in the right way. Think of climbing rope. Modern synthetic ropes do have a single filament running their entire length, but the old-fashioned ropes are made of of many relatively short fibers woven together. So there is no fiber that runs the entire length, but still different 'slices' of the rope are all part of the same rope, because of the way they are connected to each other. Admittedly, just what 'related to each other in the right way' comes to in the case of people is a more difficult question. If you want to pursue the topic of personal identity, a good place to start is John Perry's A Dialogue on Personal Identity and Immortality .

Most philosophers would I think say that what makes you the same person over time is not that there is any one thing present at each time in your life, but rather that there is the right pattern of change and the relations between different life stages. Just which patterns and relations make for a single person and which do not is controversial, but some of the relevant factors seem to be that, in a single person, features of later stages are caused by features of earlier stages in suitably normal ways. If you think about non-human cases, it seems pretty clear that identity over time does not require any 'golden kernel' present at each time. Thus we are happy to talk about a single tree that has been alive for many years, even if there were not a single atom in the tree today that was in that tree ten years ago.