Do I have to count calories, too?

Yes and no. Certainly the initial answer is "No." At the earliest stages of most low carb plans, you're switching your metabolism to a fat burning (as opposed to a carb burning) one. Don't bother with calories. 

As the stages progress, some attention to calories might be necessary. Many of us are "ex-yo-yo's". We've spent a number of years on and off very restrictive diets. Some of us have lost, or damaged, our huger-satiety feedback system. In other words, we don't properly recognize when we are hungry and when we are satisfied. For those of us with this issue, portion control is a difficult goal. Looking at the calorie content can give the missing "feedback." Some of us normalize our weight without paying any attention to calorie intake. Others need to pay closer attention to calories. Yet others find that some loose attention to calories is enough to keep them on track.