Dany not being mad before is why she didn't necessarily commit mass murder before (though you can also potentially credit that to her advisors helping to keep her in check). That's sort of the point. If people she loved were murdered and almost all her close confidents betrayed her in a short span of time in the past, it's possible she might have snapped then to and did the same thing.
Her going nuts didn't occur in a void. She experienced great loss to the point where she was isolating herself, not eating and probably not getting a whole lot of sleep by the look of her. Not that her time prior to this was necessarily a picnic, but she hasn't been put through the emotional ringer to THIS degree prior to the last season. And it took a toll on her physically and emotionally.
ANd people didn't turn against Cersi when they rang the bells ... they simply were more afraid of Dany than Cersi at that point. Again, they didn't want to be saved from Cersi... they wanted to be saved from Dany. Big difference from Danys perspective.