Is it ok for me to go back to work three weeks after having my baby?

Depends. This depends a lot on the type/complications of your pregnancy/delivery and the type of work you do.I had a Jazercise instructor work up until the day before delivery and start back teaching a week later. Some with health problems may need a couple months to recuperate.If you are healthy enough and work is compatible it is fine.
Sure. If necessary and loving, concerned child care is in place, you have to do what you have to do.And assuming you are healthy.