What's the next step in my track to become an Embedded Hardware or Hardware Engineer?
Make something.  Seriously, make something major.  Imagine this:  hundreds or thousands of people are exactly in your same predicament of getting out of school with lots of classes.  These people are largely indistinguishable from each other.  You need to do something that differentiates you from the others, and shows that you have initiative and can "hit the ground running".  

I suggest designing and making something from start to finish.  It should be as close to a real product as possible (without incurring lots of costs of fancy prototypes).  It will probably take you 3 to 6 months to complete the project.  This should also be something useful and something that you have a passion for.  Don't do another me-too project.

What I don't recommend, at least initially, is going for a masters or Ph.D.  People with post-doc degrees and no experience have a hard time getting jobs.  These folks have the education to demand a high salary, but no practical experience to actually do the job and no job history to show that they are worth the salary they demand.  In short, most employers are hesitant to hire these folks.

Once you have something other than school on your resume then you can think about furthering your education.  There is also a huge chance that you'll decide to not bother.