The 9th Mississippi was not at Ft. Donelson. I also checked Ezra Warner's Generals in Gray and Bruce Allardice's folow-up More Generals in Gray and did not find any General by that name. I do find, at CWS&SS, a "L.H. Hall" listed in the Field and Staff officers of the 9th Mississippi as a surgeon. If you don't have the compiled service record for this "L.H. Hall" you should order them. It would be nice if you ordered them through our Military Records Research Services. Just use the link at the top of this page.
As to him being referred to as a Brigadier General I would venture a guess that he was a leader in the United Confederate Veterans organization and was honored with that rank through them.
I could also suggest looking for a Confederate pension for him but due to his occupation I would doubt he applied for one. Still, never leave any stone unturned.
The Southern Historical Society Papers list the Doctors who served in the Army of Tennessee. They may show something on him. I'm having PC problems and my copy isn't working but maybe someone else can look this up for you.
Finally, Ron Skellie may be able tell you something about the Doctors of the 9th Mississippi. Hopefully he will see this message. If not you should be able to contact him from this board through his email on one of his post.