So from what I gather shipgirls grow dicks and have uncontrollable lust. To prevent them from raping indiscriminately, Shoukaku is assigned to be the official futanari cumdump.
The carriers are growing dicks as a result of an Abyssal infection. Shoukaku receives a medication that gives her immunity and also allows her to cure the other carriers by having sex with them over the course of a week. Zuikaku is angry because she doesn't want Shoukaku-nee to shoulder this burden alone, and also jealous of the infected carriers that get to have sex with her nee-san. Midway through the week Zuikaku steals a kiss from Shoukaku while she sleeps, gets infected, and later grows a dick herself.