I'm not sure you understand how this works.
Imagine there are three pension schemes A B and C.
Everyone pays into A, this is the state pension. As long as you have paid in for 10 years you will get something.
B is the state second pension / SERPS / many other names
C is the private or NHS or other pension.
Contracting out meant you paid into A and C but not B, therefore you get a pension from A and C.
People who were not contracted out paid into A and B and get their pension from A and B.
Now in 2016 the rules changed so at that point A and B were merged and you started to pay more NI.
So now your state pension is made up of A before 2016 and A + B after 2016.
But you still get to claim a pension from C. Also C is required to pay you a COPE - the difference between your reduced pension and the full new pension.
OP
If you have retired due to ill health you can apply for your NHS pension now.