Your daughter sounds just like mine, and it caused much anguish. But (touch wood) it seems to have passed. Like you, she also bit us when she was frustrated because we wanted to change her, or put her clothes on, or something else she didn't want to do. It started when she was maybe ten months when it happened once a month or so, but it really reached a crescendo at 17 months when it was a couple of times a week. She was at nursery, and bit the other children there, and although the staff were extremely sympathetic and told me not to worry, that it was a stage which would pass and there was nothing I could do apart from reinforce what they were doing - removing her from the situation and telling her it wasn't nice to bite - the manager of the nursery intervened and suspended her. (There's a whole other thread all about this in this section!)
She was off nursery for five weeks and looked after at home. She was biting quite often and it was really upsetting. Her speech is quite good, and she seemed to understand when we talked to her about biting, so we did time out, and asked her to repeat, "No biting". It took maybe ten days or two weeks but she hasn't bitten since. She started a new nursery six weeks ago and there haven't been any incidents there either.
Last weekend her friend of the same age came round to play and bit her and she told her, "No biting".
I know how upset you must be, but it is a phase and it does pass. I think it is linked to their frustrations at trying to communicate too. I don't know if it was the time out which made a difference, or that her speech and confidence improved more, or both, but it is such a relief.