Does ACC cover physiotherapy?
For an injury, usually a good part of it. Physiotherapists can lodge an ACC claim themselves, so you do not need to see a GP first. There is normally still a surcharge you pay, and it varies between clinics, which is worth asking about up front.
Do I need a referral?
No. Physiotherapy is direct access in New Zealand, so you can book yourself in. A referral matters for some specialist or funded pathways, not for an ordinary injury.
How many sessions will I need?
Nobody can tell you honestly at the first call, and be wary of anyone who does. A physio should give you a rough range after assessing you, and revise it as you improve.
Physio, osteopath or chiropractor?
There is real overlap. Physiotherapy is the most commonly ACC-funded route for injury and rehabilitation, and tends to lead with exercise and loading. Describe the problem and see who says they can help.