Well to start off that seemed like a false awakening, leading on to a very low level (little or no control) lucid dream! So well done there.

If you do that again and go into "a whole new dream" it would be a very good idea (if you're a little more lucid) to try and think logicaly while doing so, that way wour mind should be alert in the next dream which would either 'bring your lucidity into the next dream' or make you more self aware, which could lead on to an LD.