Firstly, please don't be scared as a single mum or as a woman of any status to be referred to a psychiatrist.
Also, please be aware that psychiatric services are overstretched and I suspect that your doctor erred on the side of optimism when giving you to understand that you would receive an appointment within 6-7 weeks.
It could easily be that the referral your doctor made has got lost in the mail or mislaid on arrival, and it could equally easily be that an appointment will drop through your letterbox the next week or two.
Secondly, please don't think that I am underestimating what you are going through by saying that, under the circumstances, I doubt that any covert investigation is currently taking place.
What may have happenend is that, as you suspect, a woman known to you made a complaint to your dd's nursery and that a covert investigation of some type or other was carried out.
It is probable that the investigation concluded that the complaint was groundless and that no further action was necessary.
In these cases the suject of the investigation is not told - either about the nature of the complaint or the complainant, or that an investigation is underway, or its findings, or that it is at an end, unless formal action needs to be taken.
Teachers may not carry out covert investigations into parents per se addictive but they may be asked to participate in such investigations and they are, of course, bound by whatever confidentiality protocols are in place.
Anyone who is aware that they have been the subject of a covert investigation will understandably be unsettled and may feel anxious for some considerable time afterwards.
I don't believe you are paranoid Dora, but I do believe that whatever may have taken place in respect of investigating a complaint that was made about you by a third party more than 9 months ago, whether to your dd's nursery school or to social services, NOW poses NO threat to you or to your dd.