Tell us a bit more about what kind of work, or what kind of research, you think you'd like for your career at NASA. That will give us a better idea if you are on a path to success in terms of reaching your dream job.
I will say that in general, NASA employs a lot of engineers from all sorts of backgrounds. But engineers are much more common at NASA than physicists and astronomers. As an engineer, you'll learn a lot of physics and especially applied physics to solve real-world problems, and you can always take astronomy courses as electives or on the side. The job market is much more open to those with engineering degrees versus physics or astronomy, both inside and outside of NASA.