You might inquire at the Kunming Dermatology Hospital located on Renmin Xilu next to the 医学院。

"excuse my pedantry but she does say where moving from - Australia."
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Right you are. My mistake.

And thanks for the tip on jajah. Had not heard of it. Will check it out.

Your nose bleeds are probably from the dry air, not from lack of oxygen. Try using a moisturizing saline solution spray.

You don't say where you are moving from. Skype between Kunming and the US works fine. Sometimes the recipient of the call in the US complains of the call having sort of an echo, but it is still understandable on both ends.

A final note that did not occur to me before: Please bear in mind that Kunming's airport is just on the south edge of the city. It isn't way far out like Hong Kong's or Seoul's. It only takes a few minutes to get from the airport to the heart of the city. Late at night, when you will arrive, you can literally be "downtown" in 15 minutes by taxi. So finding lodging right exactly at the airport is not as important as it might be otherwise.