If er says ankle is sprained and not broken should i go to the orthopedist anyways?

Not necessarily: As long as it is truly "a sprain" and you are showing improvement the vast majority of these injuries resolve uneventfully but can take several months. If you are not improving, question the diagnosis or are uncertain of a proper treatment plan see the orthopaedist.

Yes: You need to follow up after the injury to make sure of proper healing.

Broken ankle?: Sprains may also require treatment by an orthopaedic surgeon so yes you should keep your appointment.

Yes: Ankle fractures may take 2 weeks to show up on xray so initial er films may be erroneously negative. A primary care sports medicine physician, rehab doctor or orthopedist are the most qualified to diagnose the different types of sprains, rule out hidden fractures and prescribe a rehab program that will speed healing and more importantly prevent a common scenario or repeat same sided ankle injury.