Hi, I'd like to help you with your question.
It sounds like you are exhausted from caring for your baby and dealing with your job. Just a baby alone is a lot of new stress to handle and when you add a demanding job on top of it, you are going to be tired!
You also may not have had time to recover physically from having your baby. Most people don't talk about it, but having a child takes a lot of energy physically, especially if you had a c-section. You are talking about major surgery and you are supposed to recover from that and care for a newborn. New moms can take up to a year to feel recovered physically from the birth of a child.
You did not mention feeling depressed, but if you have post postpartum depression, that can also cause you to feel tired and down.
Just to be sure, see your doctor to rule out any physical cause (besides the birth of your child) that could be causing your exhaustion. You just may need to take vitamins or there could be other causes. If the doctor rules out any physical cause, try to develop a plan where you get scheduled breaks. It could be two hours every weekend to sleep or get your hair done, or time out with your partner. Whatever you feel would give you a break and give you a chance to regroup.
Can you cut back at work to part time? This would also help. Though staying home with your child is still a hard job, you could at least get a chance for some downtime and get more done at home so you could have more time on the weekends.
Try pampering yourself whenever you can. Buy a special soap for the shower, a cup of tea when the baby goes to bed, order dinner in sometimes, anything that makes you feel better and less stressed. You have to build these things into your day, but in the long run it may be enough of a stress reliever to help.
I hope this helped you,