OP, when you say torticollis, do you mean that she is physically incapable of fully turning her head to the left herself? Or is she more comfortable turning to the right, but is still capable of fully turning to the left as well?
Either way, I'd avoid the 'wait and see with a bit of tummy time' approach, as time is of the essence when it comes to plagiocephaly.
If it's the former (can't fully turn head), I'd push for physio or get physio privately, as I understand it can worsen in time as the muscles on one side strengthen and those on the other side weaken.
If it's the latter (can fully turn head but prefers not to - this was the case for my preemie DD), then you may not need physio, but you need to go all out with the repositioning. Be religious with it - you'll be doing it for months. You've already been given its of good advice on this. Move her head to the less preferred side whenever you can. We used to put interesting toys and lights on the less-preferred side and block off the view on the preferred side. When putting her into her cot asleep, we'd tilt her at the hips so that her head would fall to the less preferred side without waking her. Tummy time, sling time, time on you are all great (as long as the head is facing the less preferred way!).
I can't advise on the helmet, as we didn't feel DD needed one, as it had pretty much resolved by about 4 months corrected. A friend of mine's DS had undiagnosed torticollis and ended up with quite a misshapen head. They went the helmet route. At 2yo (post helmet) his head was still quite asymmetrical but by 4yo it looked completely symmetrical.