Goodness me - ok OP here is what you need to do - Planning Solicitor here. You don't need to check your deeds.
You need to contact the Council's Planning Enforcement Team, as she is running a salon from her shed, and this requires planning permission for a change of use of the land from residential to a salon. She won't have done this part, as you would have been notified as you are a direct neighbour, and so would have had the opportunity to comment on the application. Her saying that she has permission might mean she has told the Council regarding business rates, but this is a separate department completely and not relevant to the planning use of a property. I had a similar conversation with my friend, she is using her conservatory as a hair salon, and she thought she had planning permission as she had spoke to the Council, but she only had sorted her business rates.
It is highly unlikely that she would be granted a change of use by virtue of the fact that it is a residential area and the impact this type of business has on a residential area, in terms of foot traffic and parking.
The Council will be able to undertake enforcement action to make her stop using her residential property as a business, by serving an enforcement notice to cease trading. Failure by her to cease trading once served with an enforcement notice is a criminal offence, and people have been put in prison and fined for breaching an enforcement notice. So it isn't something to be taken lightly.
Also contact your local Councillor too to make a complaint as well, as they can push the Council's enforcement and planning team.
You can see any planning application and planning permission in respect of a property on the Council's website, there is a planning section and search function for applications and permissions for addresses. So you would be able to satisfy yourself before you contact the Council that she doesn't have permission.
Hope the above helps!