I am flying BLR-AUH-JFK in J (award ticket using AA miles); US citizen, no bags to check, no Global Entry.

Is there any arrivals lounge at JFK?
(My next flight from JFK is on AA, but in economy on a separate ticket, so I have to rely on EY for any access at JFK; hence this question.)

Also, the connection time at AUH is 3 hours 15 minutes.
I assume this flight qualifies for US immigration pre-clearance at AUH, and hence I would have access to the lounge after US premium lounge at AUH (after immigration clearance).
Does this US premium lounge have showers?
If not, and if I want a shower, will I have time to go to some other lounge, have a shower and then go to the US immigration pre-clearance at AUH?

Thanks in advance for any help.