I wonder whether any of the previous posters home educate? You'll find advice from those who have actually been through it will be more relevant.
I don't think you have necessarily made a big mistake, though that's impossible for an outsider to say. This is a huge change for you, and it isn't unusual to have doubts. When children first start school, plenty of parents post in the early weeks to say they are finding that transition rough for one reason or another. They aren't usually told to yank their children out of school immediately. "Stick with it, it gets better, it will be worth it" is the usual advice.
Presumably your daughter's health was really suffering for you to have decided to take her out of a school where she was happy. It isn't "just bugs" if she is constantly ill. For a child with poor resistance to illness, there's no evidence that excessive exposure to bugs is helpful. And it IS excessive exposure. Large numbers of children crowded into small indoor spaces at school, combined with the fact that many other parents feel they have no choice but to send ill children to school, makes school one of the worst places for children who are susceptible to catching things. I've known several children whose serious health conditions meant they were better off away from that environment. Your daughter deserves to be both healthy and happy.
It's early days and while this is an adjustment, you may well find that over time you will adapt to it. Can you find some things for your daughter to do independently so you can have more time to yourself? For example, in my area it will be half term next week so perhaps she could go to a tennis camp or similar activity? Ideally something outdoors, or in a large indoor space, or with relatively few children to reduce the risk of illness.
Have you found a local home ed group? If your daughter makes friends with other home ed kids, you may be able to do some playdates which will again give you some alone time. Home ed playdates can often last all day because the children have more time available. Among my acquaintance group, we often take it in turns to take the kids out to various home ed activities.
You will also get more used to having your daughter around all the time. She will get better at entertaining herself as she works through the initial boredom that comes with a big chunk of unstructured time, after being used to having her days scheduled for her at school. It is fine to tell a child of this age that you need some time to yourself, go into another room for an hour and ask her only to disturb you in an emergency. She will rattle around at first, but after a few months you will notice that she finds things to do with herself, often amazingly interesting things which she wouldn't have discovered if she hadn't experienced a bit of boredom first.