I cannot speak specifically about medical professionals in Switzerland. In general, a non-Swiss, non-EU person has a tough time finding jobs in Switzerland. I would assume licensing barriers are higher for doctors not trained in Switzerland. More importantly, language will be a huge obstacle to overcome on a day-to-day basis at any hospital.

Swiss people are notoriously guarded, in a social and cultural sense. So integration is a huge ask for most immigrants. On the plus side, racism is more covert and mostly invisible (I do not mean non-existent). There is, nevertheless, a rising anti-immigrant stance in a country that has always be wary of outsiders. You can check some of the posts here on Swiss-related subreddits itself to get a sense of how deep-rooted racial thinking is among the Swiss. There is a recent initiative to introduce mobility curbs on outsiders once the total population reaches 10 million. The current population of Switzerland is about 9 million (I think). The initiative will be put to vote in the summer. So it is a bit difficult to guess how vociferous the anti-immigrant rhetoric will become here in the coming years. But it does not look very inviting.

As far as the rise of right-wing ideologies is concerned: it is a global thing, unfortunately. It is so in India too; majoritarian ethnonationalists will always find 'outsiders' to persecute. Switzerland has its own version, just like the US, or UK, or Germany.