In the beginning, they may have froze out of pure shock. Neither of them are used to direct confrontation. Mashiro's sheltered and Nagisa was too busy studying to interact with people.
The second encounter, I think the reason why Nagisa froze and why Mashiro's afraid are one and the same. The stranger is basically hashing out their greatest insecurities and failures. Nagisa wanted to get in that school but couldn't. Her school now is not of the highest caliber but she wants to get into med school so where she's attending right now can probably affect which college she gets into. For Mashiro, she's guilty because she's gotten in the way of Nagisa's dream and probably fears Nagisa will realize she'll only continue to hold her back. Mashiro's a deeply insecure individual and while Nagisa has her own insecurities, I don't think they're anywhere near as nerve wracking as Mashiro's.
So really the new character isn't bringing about new issues. She's just made them resurface and quite impossible to ignore with her big fat mouth.
I have a feeling Nagisa will increase her studying, she already mentioned cram school I think, and lose time for Mashiro, further fueling Mashiro's insecurities and loneliness. Maybe this will give them both a chance to grow together instead of apart. Mashiro can gain independence, pick up a hobby, learn how to be a supportive partner like Nagisa has been. While Nagisa can learn time management maybe, learn not to fall into old habits of making everything about studying.
Thanks for the translation! Looking forward to the next!