Just complementing @Jacinto's answer and also answering your question in this comment.
The word you're looking for is correria and it's used as a noun (so you can't combine it with words like muito or realmente).
If you want to emphasize or intensify it, you could add words like danada. When you say correria danada, the word danada in this case means something like "very big", "very intense". So in this sentence:
Estou numa correria danada
The word danada is emphasizing how big/intense is my "correria" - I'm really busy and with lots and lots of things to do, and have a very short time to finish them.
Although "danada" is related to "damn", I believe in this case it's not used with the same meaning. But I might be wrong...
You could also use other words instead of danada, with equivalent meanings:
Estou numa correria doida/desgraçada/maluca/intensa/foda
To combine with muito or realmente, you could use the corresponding adjective corrido (masculine) or corrida (feminine):
Minha vida está muito corrida (My life is very "corrida" - it means I'm in the middle of a "correria" situation at this moment)
Minha vida está realmente corrida (My life is really "corrida" - same thing as above)
It's equivalent to Estou numa correria
Foi tudo muito corrido (Things happened very fast)
Well, there's an exception:
Ontem foi muita correria!
In this case, muita means too much. So this sentence means something like Yesterday was such a lot of 'correria'!
You could use it when telling someone how was the "correria" you had yesterday.
Nossa, tá muita correria! (Wow, that's too much "correria"!)
You could say this when you're in the middle of your "correria" (you're trying to do all the things you have to) as a complaining (that's too much for me) or just as a comment about your situation.