Hello OP,
Really sorry you're feeling low. There's a lot of completely understandable reaons for it - lockdown hell, not having your mum, very little sleep, not having usual support networks and friend. It's so hard, even in the best of times, and this is the fucking worst of times.
And I'm really cross your GP wasn't more compassionate, that's so disappointing - so many mums will be struggling right now, and it's harder than ever to access support.
I'm not sure if you have PND or not, but for me, i felt very detatched from my baby, just going through the motions of life, almost like I was an 'actor' in my own life and not really there. Does that ring a bell for you?
The good news is, there's help available if you know where to find it. Does your husband know how you're feeling and can he help you to make a plan to get more support? Can you ask to speak to another GP? Even if you don't 'have' PND, it would be good for you to speak to a GP about how you're feeling, and get a kind, professional perspective. Have you had any visits from your HV? Can you phone them and tell them how you're feeling? They should know of the next steps to take.
If, as is often the case, both these avenues are dead ends (they shouldnt be but sometimes sadly are) then don't think that you're not worth helping - you really are. There is a great charity called PANDAs who can offer advice and support, and there is a group called PNDHour on twitter, full of support from mums who have been through PND and other mental illness. Again, I don't know if you have PND or not - but even if you're feeling a bit crap, it's good to get support.
You can also ask the GP to refer you to perinatal mental health services in your area too - they are great and will be able to signpost you to any help you need.
Please don't worry about making a fuss - you are not making a fuss, you deserve support and help, and you should be a priority in this pandemic. I had my baby in October and I remember how utterly terrible it felt - the nights never ended, the sun never seemed to rise, and it felt like there was absolutely nothing to look forward to ever again. It's a brutal time to have a newborn for so many reasons - lots of love to you, and go easy on yourself x