"Internal sicknesses and problems" is short for some sort of chemical addiction, either drugs or alcohol or licorice, something like that.
Wouldn't it be sad if one of the Followill brothers was seriously into black licorice and was purging himself after going through a few bags of it before each show on the road? Just retching it all up before a show and throwing the empty bags after the groupies, screaming, "if you loved me, you'd go to Target and get me more of the stuff I like."
I don't know why, but that's what I think it is. A serious licorice addiction that has weakened the poor man to the point where he can't sing or play. How sad.