What books would you recommend I read to get an idea of world history and art history?

Joseph Campbell wrote really interesting histories about mythology, which is sort of the intersection of world history and art history. They are very detailed but readable. You get a good sense of how cultures are linked, how stories spread and change, and what the major events that shaped culture were.

H.W.Jansson’s The Story of Art is the classic text.

This isn’t exactly what you’re asking, but there’s a really neat book Art & Physics: Parallel Visions in Space, Time, and Light that goes through art history and uses it to teach about the advances in the scientific understanding of physics. The author’s thesis is that breakthroughs in art precede the thinking that enables scientists to make advancements in physics.

I actually knew the author really well as a child. It’s not a perfect match to what you’re looking for, but I learned a lot about both art history and physics from it.

It’s not art history, but I’m currently reading Powers and Thrones by Dan Jones which is a broad sweeping history of the Middle Ages of mostly Europe, although does have a chapter on Arabs.

As an English and comparative lit. major myself, I commend your awareness of how important the context is to literature and especially the history and art of the period.

Here’s my suggestion: use your reading assignments as your guide. No doubt your professor will offer background or assign some background reading, but you could do yourself a favor and go a little broader and deeper. One way is to start with Wikipedia, not to place scholarly reliance on the entry itself (although it might offer a fine overview) so much as to get to the list of references at the bottom.

For an overview, you have plenty of choices, and any of them would probably give you a good framework to place your reading in. Go for the broad view first. Always check the bibliographies for suggested further reading. Follow the ones that interest and excite you most as you (later on) narrow your focus on a style or period or author.

Also, if possible, go visit museums and see the art that was being made in the time and place of your reading. (And I do like the Janson, as @janbb suggested—an excellent substitute for a museum.)

My stated major started out as Philosophy and Comparative Literature. I was taking phil., hist., art, and language courses alongside the lit., which was both classical and European. It was great. Unfortunately I had to transfer as a second-semester junior, and then my only choice of a major was English, so I tried to construct my own phil. & comp. lit. curriculum out of what there was. If I could send some wisdom of age back to my youthful self, I’d give myself the advice I’ve just given you.

 
What are you currently reading in your courses? And what do you expect will come after your B.A.?

Sorry, my major was called Humanities and Comp. Lit., with philosophy tucked in. I loved the breadth of it and the fact that all those fields blended so well. (Divisions among fields are artificial anyway, and almost arbitrary.) Took both German and French while I was at it. Wish I could do it all over again now, just for the pleasure of it.

The World of Yesterday, by Stefan Zweig:
https://www.amazon.com/World-Yesterday-Stefan-Zweig/dp/0803226616/ref=nodl_