I think you've confused dimensions with timelines. We exist in several dimensions such as time and space, but I personally do not believe in alternate timelines. I think that the timeline in which we exist is the only timeline that has existed and is the only one that will exist.
Of course extra dimensions( more than which we can perceive) exist. As recent scientific findings show, the extra dimensions may be hidden or curled up so deep inside that it is not possible for us to perceive them at any cost. Maybe, with the speeding expansion of the universe, the curled up dimensions may become spatial. But it doesn't mean that what we can't perceive doesn't exist. And, String theory also suggests the presence of 26 spacetime dimensions for the bosonic string and 10 for the superstring!! So, We just cant avoid the fact that extra dimensions must exist and this may be well prove to be the key to the mystery behind the parallel universes!!