GH, IIRC, this is from Rambam. Note that doctors are involved in the mitzvaq of bikur cholim. R Schachter discussing the mitzva brings example of R Akiva cleaning his sick student’s house, then says – our days doctors and nurses do most of bikur cholim, we are left only with an option of cheering them up. Probably, medicine at the time of Gemora did not lead to a lot of respect for doctors, but now it is (hopefully) different.
So, from this analysis, your job of selecting a doctor is part of bikur cholim.