Yes. Under the Affordable Care Act, health insurance companies can’t refuse to cover you or charge you more just because you have a “pre-existing condition” — that is, a health problem you had before the date that new health coverage starts. They also can’t charge women more than men.
The only exception to the pre-existing coverage rule is for grandfathered individual health insurance plans — the kind you buy yourself, not through an employer. Plans like these would have been purchased before March 23, 2010; they don’t have to cover pre-existing conditions. They also may have other restrictions.