Welcome to the forum, and it's good to see you doing all you can to help your sister.
Unfortunately, a shortfall of 8 marks from the minimum score required looks like a significant gap, and I suspect you'll need a very strong case.
For what it's worth I'll give you my honest opinion.
- she suffered from a quite large burns injury on her shoulder 6 days before the test, this could have made her distressed or uncomfortable during the test as it was bandaged and she said she found it itchy, and was quite shocked immediatly after the injury
This could be a strong point, but questions are bound to be asked about why she sat the test if she was not in a fit state. Was any attempt made to seek advice about what to do in this situation?
-Financial problems, which she was conscious of, and perhaps led to a slip in class behaviour/ grades
It depends over what period of time this happened, and exactly what evidence you have to show there was a drop in her usual standards.
-Her teachers commented that she would easily pass the test and was often top of the class during 11+ sessions at the school
If, as you write elsewhere, this is not a high performing school, then sometimes a panel might think that "being top" doesn't carry as much weight as it would in a high performing school. Nevertheless, you're going to need a letter of very strong support from the school.
-I myself go slough grammar, and just passed with 110 + 1 point for my march birthday, and achieved 7 a*'s at gcse and I am currently taking the International Baccalaureate, applying for medicine and i am a senior prefect. My brother also went to the school, and has successfully run his own business
SG probably doesn't have a sibling criterion for oversubscription, but in any event it sounds as if you will have left the school by September. Family links with the school would be worth a brief mention.
-my parents and my little sister have strong links with the school, beacuse me and brother went there, and it is a 10 min drive, or 25/30 min walk from my house.
Proximity is worth a mention.
-I don't have her current levels (i will post them soon), but i doubt they are all 5's , probably 1 5 and 2 4a's.
There are lots of possible extenuating circumstances, but I fear the problem is going to be insufficient evidence of very high ability. At least 50% of your case ought to be academic, and ideally this should include three predicted 5s.
-English is not her first language, and we are a trilingual household ( english-french-urdu)
Worth a brief mention, but, if she was born in this country and brought up here, I don't think it will carry huge weight.
-goes to one of the worst primary school in slough , with very low 11+ pass rates (usually around 1-3 pupils)
There's a risk that using this argument might devalue the school's strong support.
-youngest child, so perhaps not provided with sufficiant rescourses and spoilt
This sounds speculative, and I wouldn't use it.
Her school has not done any CAT tests,
The problem, as I've said, is going to be just how much academic evidence you have.
Good luck - and do ask if you have any further questions.