If you bought HMO type policy and not a PPO type policy you need to use the primary care doctors and specialist doctors that are members of the insurance carrier's network.
Call the insurer and find out the specialists in the network -- doctors in the network are usually listed on the insurers website networked by the type policy that you have as well. Assuming your PCP (primary care physician -- weird acronym
) agrees to refer you -- suggest to him the specialist in your insurer's network you prefer.
Obamacare has nothing to do with these networks and the member doctors -- all HMO type polices are limited to approved network practitioners. If you had an employer paid group policy that was an HMO you would have similar limitations.
If you bought a local hospital sponsored insurance policy you may be restricted to that hospital's HMO clinics and doctors. You buy a ticket for their train and have to use that train's stations (more or less in analogy).