What should I do about a professor who got in my face and yelled at me?
It sounds like you were the victim of a (relatively moderate) kind of abusive workplace behavior.  I would not seek to handle this through the department-level chain of command but rather through the university level policies on such things.  

You don't say where in the world you are, but at a US university there will be something quite formalized in place about this: e.g. see this policy at my university.  Note that the prohibited conduct includes


  harassment of any nature such as stalking, swearing or shouting.


The webpage goes on to explain that any employee who witnesses this kind of behavior should report it to human resources (HR).  

You want to find the equivalent at your university.  When you report it, you should mention the name of your coworker, and they will very likely be contacted.  The rest of it is really up to HR, and they will know how to approach it confidentially and so forth.  They are also the experts on how serious the behavior is, but I think there is no question but that it is serious enough to report to them.

By the way, none of this sounds like it will be much fun for you, but I really encourage you to do it anyway.  I suspect that the likely outcome is that if this is an isolated incident, the professor in question will get nothing more than a talking-to.  But what if it isn't an isolated incident?  The community needs your help to identify and deal with the problem.