It's very difficult at this age - they save their vilest behaviour for home where they feel safest. Your DD is behaving badly by any standards although it's important to remember that at this age they are not fully formed and tend to say things for effect without any real idea of the impact they are having. Not much comfort when you're in the thick of it I know.
How is she behaving at school? often it is just at home that they misbehave while school/friend's parents have no problems.
Do you think your conversations spiral out of control? This is what we had. Things start well then become agitated. Try to keep your responses neutral (try reading: How to talk to teens so they listen and listen so they talk) which is essentially what I call therapist speech. If they say, Karen's a cow' you are better off responding 'hm, so, you think Karen's a cow' pensively, without any judgement, rather than jumping in with, 'really, what did she do god that was out of order...' Try to remember they are not interested in your opinion at any point (because you are OLD and know nothing 
).
If she starts to have a go at you, just say, how incredibly rude in the haughtiest tone you can muster and ignore her/walk away. Then refuse to have anything to do with her/start dinner/give her a lift/money/etc until she apologises. Say, I'm sorry, I'm not prepared to discuss this until I receive an apology for the tone/words you used. In this house I would like everyone to treat each other with respect. Like, really snotty!
You yourself will have to absolutely refrain from shouting if this is to work.
You don't mention any sanctions in your post. Perhaps like me you find it difficult to separate out specific incidents when it is just one long incident. I found punishments to be a quagmire that dragged me down, leaving me unable to reward good behaviour. Just work out what it is she most wants (money, clothes or whatever) and then give it only in response to a positive.
When she is calm (in the car is always good, because there is no eye contact), instigate a conversation and try and have a heart-to-heart. Maybe she is frightened about your illness and needs reassurance.
The overwhelming evidence is that yes, she will come through this. But don't lose yourself in the battle. Fight back and don't let her make you hide in your own home. Although you might want to make your bedroom an extra nice place to be and put a lock on the door, particularly since with health worries you will need some time to calm down.
Do you have any support?