I hate our new room mate

I can't stand this girl. She's messy and condescending and annoying and I want nothing more than to tell her off but I can't, because she has anxiety and depression and you can't tell someone off when they have those kinds of things. But she's so needy and I didn't sign up for this. I didn't sign up for another annoying mother or to take care of someone 24/7. Generally, if I take care of someone, it's because I love them. I do not love this girl. I do not even remotely like her at the moment. Every time we go out to do something, more often than not it's to get away from her. And I understand it's awful, I know, I feel guilty and awful about it, but it's hard not to give in to the escape when I'd rather have some peaceful and legitimately fun time and I can't have either of those with her around. Tonight she asks that we cuddle because she's super anxious and depressed about her birthday. I want to tell her to fuck off because I don't just cuddle with anyone, but that will negate everything else I've told her. I don't know how to handle her. I'm just a giant asshole and I know that, and I shouldn't be trusted around anyone with anxiety because I can't deal with their shit, it makes me so angry. Like I know they have problems in their brain, so do I. But mine make me angry. Mine make me want to tell her to shut the fuck up and deal with her problems and stop crying BUT I CAN'T BECAUSE YOU CAN'T TELL SOMEONE WITH ANXIETY THAT.
There's no help pages out there for the people who have to deal with the people with anxiety. They just say to be understanding and help out but I can't help if she doesn't fucking help herself. I'm so mad. I don't know what to do. I need to take my medication again, I think. Before I do something really bad.

Friendly reminder

If you want a good night's sleep, go to bed before three a.m.
If you want a good night's sleep and then refuse to go to bed at a reasonable time, you are a dick.
You are even more of a dick if you say you want a good night's sleep so you lock your shitty ass kitten out of your room at night and she keeps me awake all night long the night before I have an exam and a test. You, on the other hand, don't even have class until four. I think you can deal with your shitty little cat.
I have my exam in twenty minutes and all I want to do is set my roommates on fire and eat. I do not want to deal with their shit today. I am not in the mood. And dealing with them not being able to deal with each other because they're essentially children is not what I signed up for. I'm about done with both of them. Neither knows how to act like an adult and it's burning me out. I can't be the youngest one in the apartment and the only one who actively knows how to be an adult.
And don't even get me started on my parents. My mother says I'm not acting like an adult? She should look at the two dipshits I'm living with. One can't even keep her temper and the other can't even deal with working a job she already knows without having major anxiety and breaking down. I can't solve all your problems, kiddos. I am not your mom. I'm not even related to you. I have the least amount of money out of all of us, I can't afford to pay for you to go get medication or therapy and I can't be your therapist because I'm sick of your shit. And you wouldn't even know, because unlike someone, I know how to hide my anger and deal with it, and not be a little annoying shit. You know who you are.

I don't even know where to start with these two

On one hand, one can't deal with her anxiety. On the other hand, the other can't deal with her anxiety, her anger, and her problems. The sad thing is when the one with seemingly more problems is the easier one to deal with. Though I'm pretty sure she's either throwing up or crying in the bathroom right now. So there's that. Which is a whole other thing. I just need to study and focus on my own problems.