Sorry to hear about your duck. If you can't take her to a vet, do the following.
Calcium EDTA, can/ and is used often in cases of heavy metal poisoning as a chelation agent. It took me a while to find a dose, but I found one here,
http://avianmedicine.net/wp-content/uploads/2013/03/18.pdf
This site states it can be given IM, at a dose of 20-40mg/kg, twice or three times a day. I see other sources listing it can cause muscle site necrosis so you may be able to administer it orally instead. I can look into it more, but just give us her weight once you get the EDTA, and I'll figure out a dose for you.
Vet's often give antibiotics post-therapy since lead, and other heavy metals can have immunosuppressive effects. Something like Amoxicillin would work, and you can find that here.
https://www.chewy.com/fish-aid-antibiotics-amoxicillin/dp/185201
In addition, to the chelation therapy, you may consider adding some mineral oil to her feed, which may help "rid" the earring out of her digestive tract. Do not try to give mineral oil orally (PO) as its easily aspirated, which may leed to subsequent lipid pneumonia, which tends to be fatal.
Something people often under address in cases of heavy metal poisoning, is hydration. It's very important she stays hydrated throughout this. If you notice she isn't drinking as much, let us know, as she'll likely require some sort of supplemental fluids in place. I would also recommend getting a baseline weight done on her, and start weighing her daily.