Let me be the fourth person to chime in and say you can buy access to the arrivals lounge for $50. I do it regularly, even when connecting (usually to DUB). When you exit customs, follow the signs at T3 for departures (with all the construction, you have to take a fairly long walk around outside). Go to the UA ticket desk (just beside the check-in area). Show the agent your boarding pass, hand over a credit card/cash and say you'd like to purchase access to the Arrivals Lounge. He/she will process it without question and hand you a receipt and a payment slip (that looks like a boarding pass). Go back into arrivals and go upstairs and hand your pass to the person at the Arrivals desk ... and they'll show you to a shower room. And you exit feeling cleaner (and way less grubby)

.