The good news is that aerospace engineering is really just a subset of mechanical engineering, so you are in the right track. Your university almost certainly has a course for compressible flow, so make sure you take that, as it will explain a lot about the fluid dynamics involved with rockets. If they have any other electives like combustion or propulsion, just take those. As long as you can take a few suitable electives, aerospace companies will need just as many mechanical engineers as they do aerospace engineers. Alternatively, you could go to graduate school elsewhere for aerospace engineering.
