Number one, you need to find a different job as soon as possible. It sounds like nannying isn't for you. If you don't rely on the job to make ends meet, quit now. I suspect caring for a newborn is draining you emotionally and physically so you are unable to care for your own son. Not cool. Your son should come first. If you need work, start looking for something that pays better and won't use up your energy you need to properly care for your son.
Also, you may be dealing with clinical depression. It might be time to see your doctor and get a referal for a therapist. Not wanting to get out of bed isn't a good thing if your son is being neglected. You wouldn't want him to get taken from you. He needs to be cuddled, talked to, fed, kept clean, and to be in a clean environment. If you can't maintain the basics or take care of your own basic needs, you need to get medical/psychological help as soon as possible.
In the interim, exercise is an amazing natural anti-depressant. You should go for a short brisk walk with your son every morning or afternoon to get your natural endorphins (sp) going.
If possible, find someone to help you around the house with cleaning or to give you a break so you can have a little bit of freetime for yourself. Do you have relatives in town who could watch your son for an hour or two each week, so you can rest and relax or do something fun? Perhaps take an on-line course so you can find different job more to your liking.
I hope you talk to your doctor and get help. It's your best bet.