As others have said, there is no law requiring 95% attendance.
If your child has missed 23 full days she cannot achieve 90% attendance for the full year. She will, therefore, be classed as a persistent absentee. This is a concern for the school as her education will be suffering. Even if it is 23 half days this school year, that still means her attendance for the year to date is below 90% which is a concern.
You are not being penalised for being a single mother. You are not being penalised for being a woman. You are not being penalised for trying to get a business off the ground. You are being penalised the same way as any other parent, male or female, single or part of a couple, unemployed, employed or self-employed would be.
As others have said, absence for illness is not unauthorised. However, given your daughter's level of absence, I would expect the school to want proof that these illnesses are genuine and justify keeping her off school.
If all the absence has genuinely been down to illness no action will be taken against you. However, your post suggests you are keeping your daughter off school for every minor cold. That is not necessary. Advice from the NHS is that she should only be kept off if she has a fever. You should send her to school with a supply of tissues and encourage her to throw away used tissues and wash her hands regularly.
I'm not sure where the £1,000 fine comes from. If the LA take you to court for failing to secure regular attendance, you can be fined up to £2,500 and/or sent to prison for up to 3 months. If they don't take you to court, the most they can do is fine you a fixed penalty for each unauthorised absence.