Sammiez it's very brave of you to post here and it's good that you have insight into the relationship dynamic that's developed between you and your daughter. So many people don't have that insight.
You say you can't afford counselling and you're scared it won't work - I wonder if there is a service in your area that you could use, such as a free government Parenting Service? The professionals there, at least, will have a good body of knowledge regarding parenting and its intricacies - whereas a general counsellor may not. Also, a dominant model at the moment in parenting intervention approaches is an attachment-focused model, which is all about relationships and affection and meeting your child's emotional needs, rather than simple behavioural methods which aren't going to address the issue in your situation.
I do think it's important for you to try to get help for this because attacking your daughter on an emotional level - e.g., put-downs, using her previously confided emotions against her, etc. - can be very damaging. I don't want to make you feel guilty in saying that, but I believe that the most important thing parents can do is provide an emotionally "safe" environment for their child - assuming that the child's basic material needs are met, such as food and water, a safe home, what they need for school, etc. I think that a child from a poor family which is emotionally warm and supportive will be much more secure and have a better "developmental pathway" than a child from a well-off family that buys the child lots of things but is, in whatever way, emotionally dysfunctional. In my work I see parents who buy their children the latest gadgets but aren't there for them emotionally or manipulate them emotionally and it can be so damaging.
So anyway, from what you've said this is my perception of what might be going on. During the time you were pregnant and when your daughter was in her infancy, she was a "blank slate" full of possibility. You wanted everything for her that you didn't have yourself, and you didn't want her ever to be hurt. Maybe you felt that you would always be able to protect her if something went wrong, and fix any problem quickly so that she could continue to live a happy life and have the life that you dreamt of for her. But it sounds like now your daughter is a bit older, she is letting down these dreams you had for her, and disappointing you. She is clashing with other children and has become a target for bullies, she is needy and demanding and whiney. Initially you thought this was just a little blip that you could help her to overcome but now you may feel that these seem more like stable, enduring personality traits - and you're angry at her for being like this and angry that the childhood that you'd imagined/ idealised for your daughter is not the childhood that's unfolding for her, and yourself. And maybe you blame her for it or maybe you think it's a reflection of yourself... maybe it's even tapping into insecurities that you have about yourself or your childhood... and you feel inadequate. All this makes you feel unbearably angry and you take it out on her.
I don't know how accurate the above speculation is. But the reality is that your daughter is your daughter, she comes with the temperament that she has... but as a parent you can do a lot about her upbringing/ environment to try your best to help her to flourish, or to fail, with her innate personality. And in order to flourish she needs to feel emotionally supported and secure. I wonder if with your anger and with lashing out at her, you are trying to get her to "see the light" and "change her ways" and be successful and a more comfortable fit for you - when in actual fact by being warm and supporting you could achieve the same goals but also ensure she feels loved and secure, which is so important.
And again, it may help to consider your own expectations - of what your child would be like, of what motherhood would be like, of what your daughter should be able to do - and evaluate whether they are reasonable, because they probably underlie a lot of your anger. Can you change any of your expectations so that you don't feel like they're always being let down? For example, a reasonable expectation might be, "Each child has a personality of their own that parents have no way of predicting - my job as a parent is to embrace and nurture that personality and encourage my child to reach her full potential" rather than "My child SHOULD be able to... [insert what you expect of your daughter]".