My take on time travel (which I obviously have no supporting evidence for) has always been that it probably creates an offshoot timeline at the moment you go back to. So if Barry went back to save his mom, he'd be in a new timeline where she lives, but all the people he left behind wouldn't notice any difference at all...except that Barry is just gone. From their perspective, nothing about their past would change, because they've already experienced it. Also, if Barry saves his mom and then goes back through the wormhole, he's in the parallel timeline where she has always been alive, so everyone remembers her being alive anyway, which has always been their history. It didn't change, it was always like that. He just thinks he's changed it, when in reality all he did was hop timelines. He's just abandoned all the people he knew to a life without him, and traded it for a group that never knew anything but his mom being alive.
Like the episode with the tsunami. There is a timeline out there where Iris and everyone else died to the tsunami, Barry just left that one. Now you ask, why aren't there two Barry's in that timeline then? Well, it is also entirely possible that the timeline he hops over to is created instantaneously at that moment when he hops, so there is no paradox of two Barrys.
That's how I imagine time travel works, which has always made me view time travel in a lot darker way. You aren't saving the people in your timeline, you're abandoning them to death or whatever fate you're trying to prevent. Because I don't feel that a timeline simply winks out of existence because one person leaves it. Your frame of reference changes, that's all.
Obviously this can be argued to death and I wouldn't have answers for things like our Barry seeing future Barry telling him not to save her, but I still feel that it can be consistent with my creating new timelines theory, it just gets more convoluted.
