Point out you are doing exactly what she asked and if she doesn't like it, she shouldn't have told you to do it.

Housemate sounds like she needs help because she’s not taking things well at all. Maybe suggest a compromise of chatting to her when she initiates it in the meantime?

Point out the stress, mood swings and that there is professional help with those types of issues. It really sounds like her hormones are going crazy, and this is important for anyone with female hormones to follow up and keep track on them. If she lashes out then point out that this is also another mood swing and start looking for another place or new roommate, make sure she understands Roommates doesn't mean friends, family or even acquaintances. You just share a place, that is all. You do not have to communicate, and definitely cannot take out your issues on each other.

next time she yells at you reply sternly with "you good?", or whatever you would say in place. but make sure you are not timid or yelling. I have younger brothers and it tends to stop them in their tracks and usually gets them to think long enough to explain what's actually wrong. sometimes it takes someone acting like a parent to snap people out of acting like children when they are in bad moods.