I speak and read to my children in Spanish, and my spouse speaks and reads to them in German. Our common language when we met was English. We lived in various countries for a few years but now we live in the US. I'll base my answer on our experience raising bilingual children.
You can indeed read any book to your child in your own language. For the simplest books, you can wing it -- i.e., make up your own language version as you go along. Eventually you'll get to books where you'll want to spend a few minutes on your own doing a bit of preparation, so that you feel happy with your version. This is not cheating. It's perfectly fine to do this.
Later on, if your child finds the English text distracting, you can put an index card over the English. This is a case where a bit of advance preparation can be helpful, so you can remember what you wanted to say on a particular page, without having to lift the index card.
I recommend the books about bilingualism in children by George Saunders. These books helped us feel more confident about what we were doing, in the beginning.
In late elementary and early middle school, I sometimes did need to read to and with my younger son in the original English, for some assignments for school or for personal interest. In these cases, I liberally commented in Spanish as we went along. That's okay too. For example this is how we read The Autobiography of Malcolm X.
At some point I had some fun adapting some English texts to Reader's Theater scripts in Spanish. This is fine too, as long as you don't publish your scripts! I used them for an after-school Spanish literacy project I did with my older son and some other bilingual children. I selected easy readers from the library that had a lot of dialog. These Reader's Theater scripts in Spanish were very helpful in helping my children develop fluency in reading in our language. And it was tremendous fun for everyone. We even performed one of our adaptations at the public library once, and took it on the road to perform at Spanish-speaking family day care providers.
Here's a tip. I made a point of teaching my children to read in Spanish before it was time to start reading in English in school. This was very helpful.
By the way, some children mix their languages when speaking until age three or even later. This is nothing to worry about. If this happens, just make sure that you consistently answer in your home language, and the child will sort things out eventually.
When you are out and about, do not let anyone make you feel embarrassed about speaking to your child in your language in front of others. Sooner or later you'll encounter someone who'll have a hard time accepting it. But this negativity comes from ignorance. Just ignore it.
Don't forget to see what's available in our own language in your local public library and also in the school library system. Some libraries have good collections of children's books in other languages.
You may also be able to find children's books and stories in your language on the internet, published in such a way that anyone is welcome to download and print. The Mexican government, for example, has a lot of these free texts online.
Remember that basically, reading to or with your child is an opportunity for physical, emotional and intellectual closeness. You can use that time to solidify your bond, build cultural knowledge, and entertain! Therefore, feel free to use the pictures in the books in any way that works for you. You can use the published text as a basis for telling a story in your own language, or as a jumping-off point for whatever you like.