I came at this book backwards in the Verghese bookset. I read "Cutting for Stone" in 2011, apparently right after it came out, and found it to be a beautiful story, and the writing itself was spectacular and at times breathtaking. There were sentences that I would reread just for the joy of the words. "My Own Country" was recommended by a friend recently, so I picked it up. It's a different beast altogether; a memoir rather than a novel. It was written 15 years before "Cutting for Stone". The story is engaging, although solemn. It is an interesting journey of a doctor reflecting on his need to have empathy for all patients, a journey made more difficult by the onset of the AIDS epidemic. His growing understanding of his individual patients was complicated by his coworkers, family, and friends, who often had very negative reactions to the same patients.
Verghese was a less mature writer in this book (published 15 years prior to "Cutting for Stone"), and the writing, while always competent, is much more straightforward and factual than in his novel. This may well have been by choice, given the subject matter.
It's a fine book, and I enjoyed it. Set your expectations; it's not the soaring, emotional prose of his novel. And, really, that's okay.