do I have right to choose a private nursing care home over an NHS home in Scotland?

I'm not sure exactly what your question means.

If you have such severe needs that it would be unreasonable to expect you to pay then the NHS will fund your stay in a suitably registered nursing home, just as if you were in hospital.

Everyone else comes under social services funding which is means tested. In Scotland you qualify for a grant towards personal care - if your needs are sufficiently grave. You may also qualify for attendance allowance which is not means tested but is not paid in all homes - they should be able to tell you if their home qualifies.

If social services pay for your care then you can only go to homes which have the right registration for your needs AND falls within the social services price bracket. If you pay for yourself then you can go where you want - and in Scotland still receive personal care allowance if you qualify BUT if your money runs out then social services could insist on you moving to a home within their price range unless a member of the family is willing to make up the difference.

It is really complicated and I would get advice from CAB or your local council advice centre. You can also get a guide from the library which deals with all sorts of benefits and published by the Child Poverty Action Group (it used to be when I was dealing with elderly relatives anyway).

But if you want any money from the state some sort of assessment will need to be made.

No, why should the NHS shell out on you getting private treatment?