My wife is a novelist and has written one time travel novel. It goes both ways. A heroine from the present trades places in time with her own great, great, great, great grandmother (in early 1800s South Carolina). The book then follows both heroines as they adapt to their new time and fall in love with men their prior selves despised.
She did of course have to deal with how the heroine traveling from the present to the past could affect the future, to include her own future. As you suggest, paradoxes develop if a backwards in time traveller does something to interfere with their own birth. There’s two basic approaches to this for a novelist.
- The time travel told in the story is already integrated into our past. We may not know about it, but the backwards time travel does not (and cannot) alter our present because it is already part of our history. This does limit the novelist because their story can’t have anything happen in the past that would make the present we currently understand different. That can require some clever writing.
- The many universes theory. The time traveling characters may change the past, changing our own present or future, but this creates a new and independent timeline from our own, a different version of the world than the one we know because of what the characters did to change the past. It exists simultaneous with and parallel (or whatever) to our own world. I’m not a fan of this approach because it creates an almost “why does it matter?” quality to the story.
For the record, my wife chose Option #1 for her story. And now for the gratuitous plug.