Dubai lounge access (DL SC member flying UA)

I looked and searched to find a definitive answer to this, and couldn't: I'm trying to figure out which, if any, lounges at DXB I have access to. I'm flying on (paid) United in economy.

I'm a paid Delta Sky Club member (and fwiw, likely very little, Delta PM.)
Unfortunately the delta.b*mb site is hard to parse: it seems I might have access to any of the four SA affiliated lounges, including the Dubai Civil Aviation Lounge (which apparently has showers) but it's not totally clear. Anyone know?

Separately, I'm UA Platinum (and so Star Alliance Gold). Unfortunately for lounge access, I'm UA Plat on a challenge, and so won't have a UA or Star Alliance card in hand (though perhaps my boaring pass will indicate status.) The Star Alliance affiliated lounges indicate that I need to have a Star Alliance card in hand in additon to my UA boarding pass.

What DXB lounges do I have access to? Of course I'd prefer that it be free, since I already pay for lounge access, but if I have to pay, it's probably well worth it, especially if the lounge has a shower. (I'm departing on a redeye flight after a long day in Dubai in August, and imagine my seatmate will appreciate it if I've showered and changed clothes...)