What an odd predicament to be in. Confidence is key in situations like this, so be upfront, friendly and honest. I would say something along these lines:

Hey Doc, 
The other day I hurt my big toe quite badly in an accident, and it seems that it's condition is only getting worse. So bad in fact, that I'm worried I'm going to have to get it amputated. Would it be okay with you if I swing by the clinic later today so you can check it out for me? I'm free at 2PM if that works with your busy schedule.
Thanks a bunch, see you shortly.
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