There seem to be 2 ways of not controlling one's anger in a relationship.

1. Yelling, and in the worst cases physical, release.
2. Silence.

As the first one is clearer (or even more complicated, it depends), and has less to do with your case, I'll focus on the 2nd.
The case of silence is, I think, different in the case of men and women. With Men, it comes more from not wanting to deal with it. Also, perhaps generally they are less capable, and like less, to talk about their feelings. In any case, mostly it is an escape, and is not so related to "controlling your anger."
For women, like you describe, the case is very different.
To get it out of the way, yes, for some women it is a way of teaching a lesson, AKA "The silent treatment." A stupid lesson, and again it has nothing to do with controlling your anger so I won't deal with it, but it is important to mention as people confuse not being able to speak with the silent treatment.

But then what you are describing is this complete boiling over which has nowhere to go. A silent screaming. You want to say what's on your mind but it is just too much of a whirlpool. Too much for your verbal ability, too much for comprehension even.
Is this what you are feeling?:  
The Medusian moment of petrification.

So what to do. First, take your time. Have a ready made exit strategy for these cases - say you need a while, maybe take a walk (not slamming the door behind you, just saying you need to arrange your thoughts, amicably). Then you can go and try to verbalize what you want to say and how to explain it.
You definitely don't want to go and brood and like Groucho Marx in a great Scene in Duck Soup imagining a conversation as simply a way of getting yourself hyped up, where you are in the right. (The scene: Groucho is waiting for a foreign ambassador and wants to shake his hand and offer peace. Then, he starts imagining what if the ambassador doesn't want to shake his hand, why, his hand isn't good enough, and so on upsetting himself, and then the ambassador comes, gives out his hand only to be slapped by Groucho yelling so it's war you want!  (I'm sorry but I'm describing from memory, from about a decade ago.))

Understanding him does not mean agreeing with him. Though it's obvious that you are in the right, still as he mistakenly thinks he is in the right (don't we all), you should try to think like him and understand where is he coming from in order to respond well. Even if you don't convince him (sometimes people are known to be stubborn) the conversation can move to be on calmer notes.
Also, try to remember you still like eachother while reflecting on the situation., and think of some things you do like about him.
 
As i'm sure you had had more than a couple of arguments, notice yours (and his) behavioral patterns and learn from the past. Know better how to respond the next time one occurs.

It is not easy to verbalize, but there aren't a lot of better ways to get your anger out than by expressing it in words. Expressing in action is rarely a good idea, and I must say, a much less effective release than actually managing to verbalize what bothers you.
Sometimes, it can take quite a while to get to a deep understanding of what bothers you. Depending on your character, you might try to write a story with the people involved as the main characters (though usually it is good to change the scenery). Sometimes that helps.

Of course, if you are upset at the moment, all this won't help. But if not, like going into the wilderness, preparation is good, and then when you run into trouble, and one usually does, you'll be more likely to handle it better.

Films Discussed

Just a small remark. I think if you are in a relationship, then it makes an enormous difference if you are physically close to the other person during the argument. The moment where someone gets upset and shifts away and crosses their arms is usually where the escalation begins. Likewise usually you can tell that you are very upset when you don't want the other person to touch you.

Maybe you can try to get into the habit of talking while touching each other, or holding hands. It requires both people, but you both take on a different tone, as significant a change as the difference in tone that adults take on looking delightedly at some adorable baby.  (Though perhaps not that particular tone, however.)