Yeah I was going to suggest the same thing that Mr @Rod_Knox did… with draining the fluid and adding an “intermediary” fluid like a light motor oil to basically serve as a diff flush. Then just refill with the proper lube. Its a good idea.
What is not a good idea is waiting for some fancy analysis… what do you expect them to tell you? Its not like an engine oil analysis that can tell a myriad of things… You have water in the diff… get it out, right away, sooner the better.
In my prior post I mentioned the worst thing that you could do is to leave it in there and also not drive it…that gives it time to separate and or dry the bearing surfaces out etc… Just drain the fluid… immediately.