Story is very careful that it is just a very different (alien) perspective of mundane (no time travel) happenings. I haven't seen the film yet, but by all accounts it includes events requiring time travel (or retrocausation), which is definitely not the case in the story.
I would be much happier if she just got incredibly smarter after the interactions. I can see so many plot possibilities arising from that.
(People start distrusting her; she starts feeling more intimate with the aliens then humans; etc)
It resembles many programmer's belief that there just may be a 'holy grail programming language', where translating abstract thoughts into working code gets much easier, and your thoughts themselves are shaped by the structure of this language.
It might be arguable that Turing-complete languages in general are the holy grail, allowing expression of any algorithm into code. But indeed our productivity has risen so much with modern languages compared to the very first Turing-complete languages that one does wonder how far from optimal-human-productivity our languages really are.
The same musings naturally apply for human language of course :)
Also, the movie didn't bother to really explain this – though it made hints with the statement about how the heptapods see time, and Hannah's name being the same forwards as backwards, etc. – but there's no time-travel aspect specifically because there's no influencing going on at all. She doesn't cause anything to happen.