First of congratulations! You sound like a wonderful mum already. Its completely normal to feel overwhelmed in those first few weeks as you adjust to motherhood. I'm a single mum with a six month old. I promise it gets easier. I also found it very hard to accept help, I've only ever left my daughter one time for 25 mins. Every baby and situation is different but some practical advice that worked for me....
After a few weeks of no sleep I was completely burned out (my daughter would only sleep on me and never in a moses basket). I nearly fell asleep whilst breastfeeding and so I decided to make my bed safe for co-sleeping just in case (I hadn't planned to co-sleep). Eventually I had to balance the risks, when she was about 6 weeks we began co sleeping and everything got better. I slept 8 hours a night and my daughter was well rested and much less grizzly. It is and always has been so much harder to get her to stay asleep when she is overtired.
Remember this, you are exactly what she needs. Don't feel inadequate. Babies don't need much. To be fed, clean and warm. Your job is to keep them safe and give them love. Rock and sing to her, talk to her and tell her how loved she is.
I would go out with her every day. Just a short walk in the pushchair. She enjoyed that and the fresh air was good for my mental health. As you get more confident you can grab a coffee, pop to the shops, go for a bus ride. Each time you do something you feel a sense of achievement and you grow in confidence.
If people offer to help, ask them to help with cleaning, laundry or shopping so that you can focus on the baby.
Do you have a children's centre, or a community midwife? Speak to them. They can signpost you to support services. Don't forget to watch out for signs of post natal depression, it can happen to anyone and the earlier it's identified, the better.
For those first few weeks it is survival, just do the best you can. After that I would really recommend finding some mums, going to baby groups, the library, or stay&play. It can be very isolating as a single mum. These groups really helped me and I have a better social life now than I've ever had.
Congratulations again. I am sure you are doing better than than you think!