There is a small animal clinic at the vet school but that's over in Columbia. Here is a list of some vets that may be able to help. There are some in and around St. Louis. I would call first to see if they have experience treating bearded dragons. http://www.anapsid.org/vets/missouri.html
That's a bummer. University of Illinois is a bit further, in Urbana, but they take excellent care of dragons and I bring my guys there when they need advanced help. As I mentioned though, do check out some of the local vets on that list for basic treatment first.