Do you have a photo of the Amoxicillin package you are using? For a chicken - Amoxicillin dose is 57 mg per lb. (125 mg/kg) 2X a day.
Does the scab/lesion extend to inside of the beak or is it mainly on the outer edge?
@casportpony and @Eggcessive may have better ideas and chime in, but you will need to see if you can express as much of the pus out as possible. As you found, chicken pus is a semi-hard cheese like substance and won't dry up - it has to be removed. If you have tweezers to help you remove the pus that would be good. Since it's right next to her beak, then flushing it out with sterile water might be your best best.
Does the scab/lesion extend to inside of the beak or is it mainly on the outer edge?
@casportpony and @Eggcessive may have better ideas and chime in, but you will need to see if you can express as much of the pus out as possible. As you found, chicken pus is a semi-hard cheese like substance and won't dry up - it has to be removed. If you have tweezers to help you remove the pus that would be good. Since it's right next to her beak, then flushing it out with sterile water might be your best best.