Doctors' salaries start at $200,000 and can easily exceed half a million or more. Although let's forget about this and remember the plot.
Well, that really depends on which country they live in. And if Ocean decides that they are in a country that only allows for public healthcare but not private healthcare (e.g. Canada, the land of the *gasp* maple leaf, a symbol that Ocean uses repeatedly in the game), then doctors while still enjoys a good salary, they don't make as much as you think. But like you said, let's forget about this and remember the plot.
Do you remember that Zara's father is a millionaire? Do you think he will be treated in a cheap clinic for the poor or choose the best one with professional doctors? Here's your answer.
First off, all doctors are professionals, even ones in a "cheap clinic".
Secondly, when you have a bike accident serious enough that they are talking about amputation, you don't get to choose which hospital the ambulance takes you to. (In fact you might not even be conscious at that point.) It's extremely likely that your injury demands that you are taken to the nearest available hospital to be treated asap.
Why did you decide that Nojiko lives in a middle class neighborhood? Although with all these alterations by Ocean, you probably forgot how Bella was making fun of the MC and the place where he lives.
The issue of Nojiko's financial capability is indeed a bit of a weird one.
On one hand, putting 2 kids through private college is not easy, especially for a "single mom", even if she's an MD. Also, it's possible that she had a career change and only became an MD not too many years ago, and is still paying off her own hugely expensive tuition. Granted, it's not the common scenario, but it's not unheard of neither. A fair number of doctors started out with a first career as a nurse before studying to become a doctor for a second career.
On the other hand, a non-specialist general surgeon MD shouldn't be able to override an amputation decision. That's typically a decision for the specialist on the case. And if Nojiko is already a specialist and was able to handle Nick's injury without amputation when all other doctors said it's not possible, then she should indeed be some kind of "senior figure" and it wouldn't make sense for her to be a "newbie" that is financially struggling so much that she's living in a rat-infested house.