You may want to buy 'medical payments' coverage to pick up the amounts your health insurance plan does not cover. But don't worry, many insurers will cover you despite a previous decline.
Some companies are just stricter than others.
We can recommend the right companies for you. Most insurance companies do not mind if you are on a common medication. We will steer you to those insurers that will treat you fairly. Most insurance companies will underwrite a case that has recent illnesses or injuries if those are resolved with no further treatment needed. Even some ongoing problems can be covered right away, such as controlled high blood pressure or hypothyroidism.