Sorry to hear that your experiences with support services have not been positive in the past but, although you say you don't see the point, it would be worthwhile seeing your GP again to talk through that.
Funding to mental health services has been cut drastically, which doesn't help people in your situation. Mental Health Nurses are brilliant at what they do but, as with GPs, they often treat the symptoms and not the cause. Counselling could help you to get to the root of your depression and anxiety and, hopefully, help you with strategies to manage it.
I can understand your worries about Social Services but a depressive illness and anxiety does not mean you are an unfit mother. From what you have written it seems you are coping amazingly well, under the circumstances and, if there are no safeguarding concerns (risk of harm to a child), they would not think you an unfit mother. They could even help by giving your GP a nudge towards referring you to appropriate support services.
It is a shame you cannot speak to your partner but keeping your feelings bottled up is not good, I speak from experience here Lady_Bird, I kept things bottled up until I nearly cracked and I am now taking medication and having counselling; the jury is still out on whether it is helping but without it I could possibly be a lot worse. As I said before I hope coming here helps, it is a good place to offload to others who have some understanding of what you are going through.