Well I am glad to hear you have a support network. Definitely use their help as much as you can. I used to leave the children with my husband and have a bath daily in the first year of my daughter's life. It felt like the only way I could get time to myself to relax for a while, otherwise I wouldn't be able to stop myself going to help (although it did get cut short occasionally!). Try and give yourself some time each day to do something you want to do, it really will help you start feeling better.
I also used to take my oldest to do something just us two together once a week or so, too. Even just to pop down to the shop to buy a chocolate bar, a quick trip to the park, occasionally something longer like a trip to the cinema. This helped us have some uninterrupted time together, like we used to. As he got older, he just kept wanting his sister to be there too. It was heart warming to hear that.
My children are 21 months and 3 years old now. So it's almost two years since I was in your position. Life if so different with two, they have such different personalities and both keep me on my toes. What worked for my son doesn't work for my daughter. She has still never slept through the night and he is a brilliant sleeper. You initially think that because you have done it once you know what you're doing now, but I had to reset my expectations and learn all over again with my daughter.
It's harder to get around, harder to keep the house clean, and harder to keep everyone in the house happy all the time. It took me a lot longer to get used to being a mum of two, than it did to get used to having my first baby. But overall I love it now and I wouldn't change it for the world. They have a beautiful relationship, and my son calls her his best friend. They read stories together, and colour together, and sit on the sofa together to watch TV. I love that we brought a little best friend into the world for my son, and that she has him to look after her. Don't get me wrong they do fight and argue regularly!
I really hope you start to fell better soon, and that it's just your hormone levels causing the baby blues or something (I had this for three weeks after the birth). But if you feel that you can't shake the feeling of despair and hopelessness, please go and see a doctor. It's nothing to be ashamed of, and very common to need some extra support.