I needed it so bad is good colloquial English, but it's less used because it has a much stronger feel to it.
I've been thinking about when it would be used, and I reckon that taken literally it would be appropriate for a drug user talking about a late fix... Of course, it's frequently used ironically, for example when you finally get a beer on a hot day and in similar situations when you want to exaggerate your need. For an emotional statement like the example given though, you probably wouldn't want to exaggerate your need. But I can well believe I needed it so bad would translate ne avrei avuto tanto bisogno in many situations.
We don't have any context so we don't know what chiara really needed, but it was probably some emotional support. Also I think we're more than likely to email than write nowadays. A loose translation might be:
I was hoping you would call or email me in the last few days. I really needed some emotional support.