It appears to have been left intentionally ambiguous as Joe Kelly reveals in this interview.
How much changed between the graphic novel story and the movie’s script?
Kelly: The story is fully intact. The changes are all in how Barbara’s internal life is externalized. In comics, we can play with form in such a way that if she speaks to fairies or things happen in front of other characters, we can still maintain the “Is it real or not?” question.
In a film, though, certain bits are complete “giveaways” in one direction or the other. It was critical to Anders and myself to maintain that question for the audience, so all of the changes are meant to keep them guessing and keep Barbara’s reality intact.
Collider, ‘I Kill Giants’: Joe Kelly and Ken Niimura on Bringing Their Award-Winning Story to the Screen
Of course Sophia could have actually seen a tornado and just misidentified it or been playing along to please Barbara. In fact the style of the giants and Titan were explicitly chosen to look natural and "of the environment" which plays into these theories.
NFS: What served as your primary inspiration for the appearance of the monsters in both the comic and in the film?
Kelly: That was all Ken Niimura's genius. He's an incredible artist and meticulous designer. We went through a lot of designs of giants and the Titan. We were both fans of Shadow of the Colossus, which helped inform the Titan. Mostly, we were looking at things we wanted to avoid. The classic version of a giant as a "tall man dressed in peasant's garb" was our "no-fly" zone. Ken just went wild from there.
For the film, Anders took inspiration from Ken, and then being an artist himself, started doing designs of giants that were even farther afield from what we'd done in the book. We wanted creatures that truly were of their environment—asymmetrical, of the natural world, etc. The design team really came through for us, especially with the Titan.
No Film School, 'I Kill Giants' Screenwriter Joe Kelly on How to Adapt A Comic into a Successful Feature Film