You don't have to write down absolutely everything. However, as my high school Algebra II teacher always advised, "The more you write down, the less room you leave for mistakes."
There are three main benefits to showing your work. One is that you can backtrack in case you notice that something is wrong later on. Isolating an error is much easier this way. Otherwise, you would probably have to start from the beginning and re-read the question.
Another advantage is that your mind is clear and focused on the question. In a sense, writing down every step serves as a confirmation that you know what you're doing. Another benefit, related to the first, is that you place yourself in an active mind frame. Simply assuming something is passive, and that will get you into trouble during the GMAT. The test, whether in DS or CR, lays traps for you to passively assume things. Never assume anything on the GMAT.
If you're worried about timing issues, then it's all the more important to start practicing by showing your work now. You have plenty of opportunity with the OG and GMATPrep. Overtime, you will gain speed to the point that it won't present a problem on test day.
Get the best GMAT Prep Resources with GMAT Club Premium Membership