My son also had torticollis (or however it's spelled) and developed a flat spot on his head. His ears were very slightly mis-aligned. We got him started in physical therapy for the torticollis. As far as the flat head was concerned, we'd heard that the problem could self-correct over time. But, we wondered, what if it didn't? If the helmet is to be used, it must be done before the baby gets too old and the skull is no longer malleable, so we knew we had a time limit for our decision. We stewed and stewed about it, but finally decided to go ahead and get a helmet for him. To our relief, it didn't seem to bother him at all; he wore it 23 hours a day for about 3 months. He didn't get his helmet until he was closer to 5 months old, even though we'd gotten the script for it when he was 4 months old... his head control was not stable enough at 4 months to tolerate the added weight of the helmet. But by 5 months he was good to go. I think the age of starting is different for every kid, depending on where they are in their development.
Of course, my son's head shape may have corrected on its own. But we were glad that we'd taken some proactive steps. You'll have to decide what you're comfortable with doing... mostly I wanted to share my experience so that you know that a helmet is not as bad/scary as it looks.