This is Dr. David
you need to see an infectious disease doctor and get that pus cultured in a lab to see what bacteria is growing under the skin
some infections can be resistant to certain antibiotics such as doxycycline. you might need another type of antibiotic to help clear this infection
you should rest the finger for now and avoid wood work as much as you can
you should elevate the finger up on a pillow above your heart as often as you can to help decrease swelling and pressure.
you can also ice the finger to decrease pain and swelling.
it doesn't sound like you have had a skin or wound culture yet by your doctors.
let me know if you have other questions.
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