First, eating her buggers is NOT making her sick. Remember the buggers are coming out of her body. What's already in her body is what is in the buggers.
Eating buggers is common. I remember doing it when I was a kid. My 9 yo granddaughter still does it. She has learned to do it for the most part in private. All of us have just made a face and said "gross" or something similar. I don't know of any way to teach a child to not do that because I think it's not worth spending a lot of time on it.
The reason they eat them, I think, is because they taste salty. My 6 yo grandson, who has stopped eating buggers, I think, or he's more clever about doing it in private. But.....he licks our skin. Again, salt.
He was at my house today and drank 1/2 cup pickle brine. I have to hide the salt shakers so that he won't lick them.
I think that my daughter stopped the eating of buggers by handing him a tissue every time she sees him picking his nose. He stayed overnight with me and woke me up to get him a tissue. :) My daughter just ignored my granddaughter at the beginning. Maybe if she'd been handed a tissue along with the "gross" she'd have stopped by now.
I outgrew it and so will today's kids. I look at it as just a stage.
You could try keeping her nose well lubricated. I catch myself picking at my nose when it's dry. I use a sterile mist that comes in a small spray bottle like medicated nose spray. I know Little Noses carries it but I get mine for much less at Costco. You can also get a generic brand for less than Little Nose's at a drug store FM or ----.
As I recall we also had my grandson blow his nose freqently, sort of like potty training. We just wiped it until he learned to blow. My granddaughter still has trouble blowing her nose but she has learned that picking your nose is done in privacy.
I don't know how old your daughter is but if she's in daycare with several babies/kids it's common to catch everyone's bugs. They pass them around. My granddaughter ended up in the ER a couple of times and hospitalized once before she was 3. But she has cold induced asthma. The sick kind of cold not the temperature kind.
I know it's hard to believe but it's good that kids catch all these bugs early. Their body builds up an immunity so that they are more likely to stay healthy once they're in school.