Please don't worry, I have carers everyday as I'm permanently disabled. It took me a long time to ask for help as i am a single mother, at the time with a baby, now with a preschooler. I was terrified they would take my baby. Absolutely scared stiff. And I was convinced that if anyone told them I was depressed as well as physically disabled, they'd think I was an unfit mother and subject me to all sorts of assessments and jumping through hoops.
It turns out that they can't legally can't take a child away from a parent purely because of being ill. But also really don't want to as it would cost them a fortune, as well as not be good for the child. They have to act in the best interests of the child, and taking a child away from their sole care taker where there is no abuse or neglect would do untold harm.
So basically, don't worry. I researched this to the nth degree :)
Have a think about what kind of help you might need. Would it be the stuff uoud nornally do like household and personal care help? Like, tidying, cleaning, meals, helping you run a bath / get in and out, or being your hands and back, lifting your dc into the bath etc? Or would it be childcare? I don't know the age of your child but from the sounds of it, more help in the home than childcare/ babysitting type stuff?
As a first step, it should be adult social services who help you, as you need help with your needs, and one of those needs is your parenting needs.
This is where you have to stick to your guns a little, as all departments would rather finding came from a different department due to all the swingeing budget cuts, so adult social services may try and throw you over to childrens services. Some may say that if it involves a child it must be children's services, but that's not actually true if it's about helping you do stuff for your child.
But as its temporary, it probably doesn't matter who ends up helping as long as they provide the kind of help you need, and they understand these needs are solely due to you having an operation.