Ok, not to be yet another self-proclaimed TSR therapist, but this doesn't seem to be a very healthy way of approaching education from your mother. Whatever happens she should be backing you as long as you have given it your full effort.
That being said I can understand to an extent where she is coming from. Grammar schools do have a very good reputation for a reason, and it is something that is a good goal to have. Now I can't tell if she's pressuring you because she feels she has the parental duty to give you the best start in life, or because she wants to impress her friends as you mentioned, but either way from what you have said it doesn't appear as if her reactions are appropriate at all. It's a really tough situation and I can empathise as to what it feels like to disappoint your parents in terms of academics sometimes. Equally, I don't know her situation and how she grew up, and what her ambitions are for you, but the bottom line is that the way that the situation currently is is quite unhealthy. Feeling disappointed is a natural response to failing at something you wanted, but the fact that you are crying over something you aren't even sure you want is, in my opinion, indicative of her trying to fulfil her own ambitions through you. Again, not 100% necessarily a bad thing, but it all depends how it is done, and from your description it doesn't seem like she's going about it properly
I'm not so sure it's possible, much less a good idea, to try and lessen her expectations. Rather than doing that, I would suggest you change your approach and tell her you are gave it your best shot, and for better or worse whatever your results are is what they are. I don't suppose you constantly trying to convince her that you won't make it is doing much to help the situation, true as it may be (I mean it may not be true - remain positive). Rather, focus on the fact that you put in as much effort as you could and be prepared for your next steps, be it grammar or public.
Good luck however results day goes.