No, there is not a jealous Shimamura arc. Shimamura does note that Adachi is very attractive, and even mentions that she should be the one worried about Adachi being stolen from her rather than the other way around. Despite that, Shimamura doesn’t genuinely express jealousy regarding Adachi in the LNs. However, Shimamura does later become more affectionate towards Adachi. I wouldn’t call it “overly affectionate”, but it is still definitely a big improvement over what’s been seen so far in the manga adaptation. The light novels reveal a lot more of Shimamura’s internal monologue, and in Shima monologues from later volumes, Shimamura expresses (very straightforwardly) how much she loves Adachi, how much she admires her good qualities, and how adorable she finds Adachi’s mannerisms to be. I would highly suggest reading the whole light novel to get the most out of AdaShima. Thanks for reading this, if you did.