General information, not specifically for the OP.
Asking locals is probably a waste of time. A new patient is unlikely to get a quick appointment.
Urgent care facilities typically have the ability to book quick appointments.
Hotels generally have lists of doctors who will see a tourist.
CHECK YOUR INSURANCE..Many insureds have network coverage. Your plan might have a national network. Your plan might have a "guest network". Your plan may have contacted rates with a different network. Might offer significant savings if you have to pay out of pocket.
Plans extend coverage in life threatening circumstances, such as a heart attack. I have no idea if an ingrown toe nail qualifies.
Some people, some medical conditions, may have to decide between paying out of pocket or waiting until they get home.