Wow, that is a once in a life time find. Congrats!
Definitely keep it wet. Everything but the stone will decay rapidly if dried.
Don't hesitate to take it to the University archaeologists. If collected on private property the artifact is the legal property of the land owner. You should insist that they acknowledge in writing that you are loaning the artifact only, not giving it to them. Also ask that they obtain your permission before any analysis/procedure which might damage the artifact.
http://www.thc.state.tx.us/archeology/aapdfs/Artifact_Collecting.pdf
That said, there is an incredible amount of information contained in that find. Materials, techniques, wood for carbon dating, etc. that can come from no other source. Ethical researchers will gladly agree to the above conditions in order to properly document the find. If they won't, move on to another researcher. Personally, I'd call the number in the above link. And so long as you know about were you found it, you haven't destroyed any data that river transport hadn't already removed. I'm an geoarchaeology PhD student at the University of Georgia.
Sheldius