I am sorry to hear that your bird is not feeling well. As birds can hide symptoms of illness until they are very sick, my best recommendation would be to have your bird examined by a qualified veterinarian experienced in avian medicine. However, failing that you can try to supplement calcium and see if that make a difference for her. Soft paper thin shelled eggs are a sign of low calcium and feather picking can result from nutritional deficiencies as well.
You can add a calcium supplement and see if this helps but it sounds like she would benefit from a balanced commercially prepared diet for parrots as there may be other nutritional deficiencies present contributing to her clinical picture.
Have you tried a pelleted or kibble type diet for her? There are several on the market that are complete and palatable and if she accepts foods other than seed it will likely be easy to get her to accept these types of food. Two brands that are known for quality are Lafeber and Harrison's. You can order these online as well as find them in high end pet stores. You can also try adding a calcium supplement and seeing if this helps her in the meantime. Calcium glubionate is available over the counter and she should get about 1 milliliter daily. She should also get access to unfiltered sunlight as she will need this to make vitamin D which will help with calcium absorption. You can supplement vitamin D3 with the diet but sunlight is the bast way to get this and its free. She should have access to 30-60 min of unfiltered sunlight daily.
Since there may be other deficiencies at play, a high quality vitamin and mineral supplement would likely be beneficial as well. Again you can find this from reputable pet stores or online. Check out the Lafeber website as they make a lot of good products for birds.
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