I understand perfectly your frustration. I myself am trying to pursue a career as a Chartered Accountant which requires DBS checks.
I can't answer your question about whether or not employers in the NHS would look past your conviction but I would imagine the fact that you were under 16 at the time of the offence would work in your favour. Moving abroad is certainly an option, but one which should not be taken lightly of course.
I think what needs to be done is more people with convictions coming out and putting more pressure on the Government to extend things like filtering even further.
Again, I would suggest calling Unlock's helpline who can do a much better job of advising you than I can.