When the Reverse Flash went back in time to kill a very young Barry Allen, he was trying to change history so that the future he came from would be a different future, a future where Barry Allen Flash never existed. He was not trying to kill Nora Allen; he was trying to kill Barry years before he would become the Flash.
Barry Allen Flash also went to the past to prevent the Reverse Flash from killing anyone.
What we see in the flashbacks of that night, however, is the Flash from several years in the future, not the present day Flash, fighting the reverse flash from the future, not the Harrison Wells version. That reverse flash is one that Barry Allen Flash will meet sometime in the future, Eobard Thawne.
When Flash saves young Barry by taking him away from the house and then continues fighting reverse Flash, something happens that somehow disconnects reverse Flash from the speed force. In the flashback we see reverse Flash stumble and fall, and Gideon, his computer, tells him he has lost the speed force. Eobard Thawne is therefore lost in the past when Barry Allen is still a child.
As a result of being stranded in the past, Eobard Thawne kills Harrison Wells and takes over his life, and in that way, he develops Star Labs and the particle accelerator five years earlier than it had been in the original timeline. According to statements Eobard had made to Harrison Wells, the particle accelerator was developed in 2020. Now with Eobard as Harrison Wells, it was developed by 2015, and as a result, the world has the Flash five years earlier than in the original timeline.
Barry Allen Flash, then, is living in an altered timeline.
I suspect that in the original timeline, Nora Allen was not killed, so Barry’s father never went to jail, and Barry never lived with Detective Joe West and his daughter, Iris. But he did become the Flash, perhaps years later than in the present timeline, and perhaps not even due to the particle accelerator.
So for whatever reason Eobard Thawne went back into the past to try to kill Barry, the result was a different timeline than the original, and if Barry succeeds in going back to save Nora, then the timeline will be restored. And this means that Barry will become the Flash without Harrison Well's interference, and that Harrison Wells was never the reverse Flash, so more than likely he will be back in Star Labs, along with the rest of the team, and Barry Allen Flash is yet to meet the original reverse Flash.