Wish I had a penny for every time I have felt like you do now! I'd be a millionaire. I am getting a bit better at it now, though.
I think what you have to do is to keep telling yourself that , although you have written a load of rubbish in the e-mail, it has had the desired result and stopped the row.(Hope it has, by the way). Your sister is unlikely to see your point of view, otherwise you wouldn't have had the row in the first place. Same goes for your Mum. As for the future, try to get better at seeing the arguments coming and either avoiding them or handling them more coolly. If you can keep your emotions in check and give reasoned arguments to people, they may not back down or agree with you, but you will not get so upset. It's hard, though. I am sure your sister knows all the buttons to press to annoy/upset you, but remember, they are your buttons and you don't have to respond to them every time. Try not to rise to her bait.
At the moment, though, you've got to try to stop yourself thinking about this row over and over. You don't need me to tell you that it will get you nowhere other than more upset. The only way i have found to stop myself thinking about something is to make myself think about something else. So, when the thoughts come into your head again, try to be ready with something nice to think about like how you are next going to treat yourself.(Doesn't have to be a big treat, some new smellies for the bath counts). Or try to remember something nice. Logic is no good with these thoughts, just stopping them is what you want to do.
Remember, you put yourself in the right, you were the bigger person because you stopped the row.
Good luck. I do feel for you.