Being sick won't keep you from getting health coverage. An insurance company can't turn you down or charge you more because of your condition. Once you have insurance, it can't refuse to cover treatment for preexisting conditions. Coverage for your preexisting conditions begins immediately. This is true even if you have been turned down or refused coverage due to a preexisting condition in the past.
The only exception is for grandfathered individual health insurance plans – the kind you buy yourself, not through an employer. They do not have to cover preexisting conditions.
If you have one of these plans, you can switch to a marketplace plan during open enrollment and immediately get coverage for your preexisting conditions.