I'm studying a medical degree so in my skills class where we have to medically examine each other (not intimately just like hands and arms and face and legs from knee downwards) there’s 2 Muslim boys, 1 white girl and 2 Hindu/Sikh girls.
Last week I worked with the white girl and a Sikh girl and because of the hand gel we use and touch each other while our hands are still wet plus natural human sweat, I got completely najis and so did my stethoscope. There was a stethoscope we had to share and I was unsure of which one to put in my ear because I wasn’t sure which side the Sikh girl had used so I gave myself the benefit of the doubt.
Basically it was manic trying to stay paak.

And this week because I was examining a patient towards the end, the two Sikhs and the white girl paired up so I began examining the Muslim guys and they examined me (hands, arms and face).

So what is it better to do? Get examined by a girl and get Najis or get examined by a guy who’s not your mahram?

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It is not permissible to be examined by a non mahrem for learning purposes usually. Therefore you should avoid this as much as possible, unless it causes you unbearable difficulty
As for the other situation, try your best to clean whatever has become najis as much as you can, but don’t be pedantic about it, and if you don’t know if something has come in touch with wet hands for eg assume it’s Tahir.