I'm sorry to see latest post by OP. you have been offered very very good advice from a lot of very experienced (some with SN children themselves) posters but you don't appear to have taken it on board at all. Or maybe I'm being too harsh.
You say she cried and doesn't want there to actually be anything wrong. Bless her. We get that. This is not uncommon. She's in denial. She doesn't want to accept it. But in time, she will have to.
So what you do is gently prod. When the time is right you talk to her. Explain that you understand how do she feels and you totally get that and it's hard when you don't want something to be how it is. Because you love her it's your parental duty to help her and supporter and you really feel that what you need to do:
.......a/b/c. And then when you think she can cope with it things you tell her that you really feel she needs to be assessed and you'll get some books to help her etc.
You say in your last post that you are not stuck. But you aren't. You are the parent and you have to parent and you have to do the right thing and you have to be proactive so you have to start doing all the things everybody has advised you to do:
speak to the GP, speak to the Senco, arrange for assessment, and buy books etc. You can do this all now. It'll take ages before any of it comes to fruition and you get any appointments. So in that time you talk to her to prepare her.
You don't just not do these because you're child isn't ready for them. (I know it's always better if a child is induce, for say counselling, in an older teen. It's almost pointless to force some children to do what they don't want to do).
But this is different. This is a medical thing she needs doing, but she doesn't really want. We get that! But parenting wise you do actually need to do this. Because she needs help and support. (She just doesn't recognise it yet!)
Even if it isn't Autism. Even if they decide after the assessment that this isn't the case for her: The fact is she is struggling. Fact. she has very bad anxiety and her social skills are not the norm. so she will need help. Of some sort. to get her to the same level as her peers.
I hope you have success.