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So what happens here is that Izuku and Luna got into their second fight after the war cuz Luna was so worried about Deku, but she would not tell him about how she felt, it's because she had a horrible nightmare about losing him forever before the war begins (plus her confrontation with Himiko Toga, her archenemy), therefore she pushed him away, leading to this argument.
In an impulsive act, Luna broke off her romance, which she instantly regrets after Deku left U.A to protect his friends. Luna fell into depression and kept pushing her friends away, yelling at them that she doesn't need any comfort or help, and gave herself a new look during that time.
