time travelling doesnt exist

this is true according to our current (incomplete) observation of the universe, and even then, some theories allow for the possibility of time travel.

travelling across multiple universes would make it so that anything you did in a unverse you didnt originate in would have no effect on your own

What you are referring to is called the Many Worlds theory. The key term here, is “theory”. It is not necessarily the reality, only one of the POSSIBLE interpretations that allows for “time travel”. For all we know, Doctor Who has the correct idea of the universe and the Time Lords are there to ensure that time paradoxes never happen.