Being shut out feels pretty fuckin terrible. I know it does. But it IS common. and while I'm sure you're not particularly interested in hearing more vague "stick with it" encouragement, I do think it's important to know that a shut out doesn't mean you need to lower your expectations. For example, last year I applied to 7 schools (across all ranking levels) and didn't get an offer from a single one. This year i cast a wider net and got into a handful of schools, including one of my "dream schools," Brown. I was still rejected from the mid 40 range schools to which I had applied last year, as well as some heavy hitters like DUKE, NYU, and U Chicago, but i had a vastly more successful application season because i had a full year to figure out what I wanted to study and find schools that fit my interests.
Also, I guarantee when you get ready to rewrite your SOP you'll look at this year's version and think, "I have so much more to say."