if you go to the docs, they might get you a physio referral - this could take weeks to come through. Did you go to the hospital straight after the accident? Sounds like you should have done.
They might prescribe you some anti-inflammatories or suggest you take ibuprofen if you can. If you leave it long enough and you still have really stiff and painful neck, they might even prescribe you muscle relaxants.
Or, you could go and see an osteopath/ chiropractor immediately and have the neck looked at - whiplash usually involves some kind of muscular damage and osteos/chiros can release some of the tension.
Teaching small children will be more potentially damaging because of the extra need to crouch/lean down, putting more strain on your neck etc.
You could also try to self-help with this - get something like ibufprofen gel, or Deep Heat, or tigerbalm and rub it into the affected area on your neck, see if it helps.