There are some showers adjacent to the UA IFL at ORD.
They have always been called "Arrivals lounge" and had open hours posted only in the morning...maybe staying open until Noon or slightly after. Accessible by First Class and Business Class International arriving passengers during this time. No access with regular United Club membership.
Access after the official hours was a YMMV situation. I was able to use them once in the late afternoon after a TPAC arrival, but others had reported differently.
Since the "arrivals" at ORD has been de-listed from UA.com, I have no idea what the status of this is.
And no, there are no shower facilities at any of the regular United Clubs at ORD.