3 months was probably too young to start. They take time to get used to being a "seperate" person - they don't know it for quite a long time, and they are used to mummy smells, mummy love, mummy food and mummy comfort - it's no wonder they can't settle themselves easily for a while. Also - the ability to put themselves to sleep doesn't even really start until about 3 months.
I know it seems the longest time, but these months pass very quickly really. I seriously would suggest allowing her to fall asleep in whatever way works best, without stress for anyone involved (on the breast/bottle, rocking, cuddling or in your bed), for another few weeks and then when she is over 26 weeks old, then you can try controlled crying again - which for me meant a cuddle to reassure you are there, in the cot when not crying, leaving to cry for 2 mins, then a cuddle again, then leaving 5 mins between each settle, which should mean not long enough for crying to get too distressed. If bedtime is right (small babies in bed by around 6.30 latest) and at least 2 hours since waking from last nap this should work. The next night, you can try leaving for 7 mins between each cuddle.
Alternatively, try picking up putting down, which can be quite hard work on the back (!) but often seems a more gentle approach, even if you pick up as soon as they get put down, putting back down the moment they have calmed down, and then repeating (often quite a number of times in the first instance) until you hear those telling yawns, and then all of a sudden, they don't bother crying any more and go to sleep. But the point is they have been reassured you are there and not far.
Sorry for rambling. Hope you find your way around this and the boxes!