It's really hard to say bc we don't know how inflamed they are, how advanced the infection, how inflamed the immediate surrounding tissues are. But after starting Baytril, you likely should see some sort of change in the inflammation within 5-7 days.
Also, don't let it bother you terribly that the Amoxi didn't knock out the infection - it really is a first-line antibiotic and just won't do the trick for many bugs nowadays.
Please do keep us posted and I'm hoping for the best outcome
!