Hemingway's English is notoriously bad. When using British colonial slang, he is out of his depth. A wallah is a (relatively lowly) worker. "That fellow". "Could you ask that wallah to bring us some tea?" A wallah in the house was like a footman, and anyone lower in status. The terms that you would most often hear in period dramas are "punkawallah" (the person who pulls a ceiling-mounted fan) and a rickshaw-wallah (in Singapore and Hong Kong). There was a time in Britain when Indian princes and maharajas were society darlings and the counties were full of retired civil servants from the colonies. That was the time when Indian words would fall from the lips of very English people. An Indian word that has survived well in true-blue English is "pukka", meaning "first class" or "absolutely genuine".

It means medical people in general. 'Wallah' is upper-class British slang from the days of the empire in India, and refers in general terms to someone doing a job. Here it probably means doctors, as it will have to be a doctor, or a least a senior nursing professional, who signs the discharge which will allow him to be moved. The term is colloquial, and slightly dismissive/disrespectful in a friendly kind of way.

"Wallah" doesn't appear to be an English word but an Arabic word. It is used to make a promise or express credibility to what they are saying. Once someone says "Wallah", then they are not allowed to lie about what they said. So in this context, "medical wallahs" could be either "medical truths" or "medical people" (such as doctors, nurses, pharmacists/chemists, etc.)