Although you can second guess yourself for why you looked, you said something important. You said that your gut bothered you and that is why you looked. We cannot explain why we sometimes feel that things are not right, but here your instincts proved to be true. What is done is done.
Yes, he will be angry with you for looking at his Facebook account, but that is the least of this as he is engaging in (at the very least) an emotional affair behind your back. This is very serious and if he is at all devoted to you this will stop immediately and he will seek help to work on your relationship.
You must talk about this with him as the knowledge (if not shared) will destroy your relationship. You may wish to do so in the presence of a counselor as this will be a very volatile discussion. But there is little choice as you now know...and will need to process this with him knowing as well. I am sorry this happened to you. Steven