Multiple timelines
I'm surprised I haven't seen more mention of the multiverse model.
There's a simple way of approaching this.
What happens to you, happens to YOU.
There is no paradox, ever.
If I go back in time and kill myself, that happened to THAT person, obviously not to me. It's a separate timeline and remains separate, and that existence goes merrily along its way, though deprived of my glorious self.
I return to my time none the worse for wear...because that didn't happen to me, it couldn't have because it didn't. Not in my timeline.
There's no changing your past. There's no changing the past you remember, the history of the world you live in. It happened. It cannot be changed. But, were time travel possible, you'd be perfectly free to go back and make as many tweaks and changes as you'd like and see what would happen.
Just for fun.
Biting the hand that feeds IT
