It's a hard age, 10 weeks. Colic is one of those diagnoses that sound medical but really just means 'cries a lot for no apparent reason'. I heard a speaker ages ago posit that it's really an emotional tool for some babies, they're creating their own 'white noise' to deal with the feeling of the world being overwhelming. Certainly in my DD's case, it wasn't a physical problem and it absolutely eased off at 12 weeks.
In yours, it's hard to say without knowing more about your situation - she could be looking for comfort, more attention, less attention, more movement, less movement, etc. A growth spurt is also common at 12 weeks.
But here's what it isn't: hunger. Formula or breastmilk are the most calorific things you could be feeding her, and you're feeding her on demand, so it's not hunger.
And if it were hunger, then adding rice, which is less calorie-dense, would be counter-productive. As others have said, it's also more difficult to digest, so if she does have physical digestion issues, rice will hurt her tummy. She's too young to process it properly.
It's hard. It's really, really hard, this feeling that you could be should be doing more for this baby that you adore. But you're feeding her, rocking her, loving her, and she's so tiny, and sometimes the only way really is through it.