Amoxicillin dosage is given orally, 125-250 mg given orally twice a day for 7-10 days. If you are certain that she will eat some egg or other food, it can be put in there. It should not be put into the water.
Baytril or enrofloxacin is a better antibiotic that treats more bacteria, including...
Can you cut into those and take another picture? It does look like lash material, and that is caused by salpingitis, inflammation of the oviduct. E.coli and other types of bacteria can be a possible cause. Amoxicillin or Aqua Mox found online can treat reproductive infection in early stages.