Look at the options for hikes other than Mt Whitney, but there is a chance you could get a "Day Use" or Overnight permit in August, if you keep trying. Cancellations show up at random times, so the more often you check, the better your chances. And cancellations will more likely show up within a few days, or up to two weeks before the week you want to go. So keep checking. Here's the website link that you need:

Mt Whitney Availability

That website requires you to enter the number of hikers before it will show you what is available. If you look at the week ahead, you will see available permits. They won't be nearly as plentiful in August, since the trail will be free of snow by then, so everyone will be trying to go.