Are you an Anthem customer? Specifically, do you carry an insurance card with "Anthem" written on it? If not, then you're probably safe.
If so, have you received an email from Anthem? Then you're probably impacted by the breach. (This assumes they have the right address for you and it didn't get spam filtered - I found mine in my spam folder).
If you haven't received an email, then contact your human resources representative through the organization you receive your insurance through.
I haven't seen anything that suggests information other than that of subscribers was affected. And if you're a subscriber, there's a chain of command. Your HR department, or whatever group you're insured as a part of, should be getting official communications on this, and should pass them to you if you ask. And you can always call the number on the back of your card, although you'll probably just get generic statements matching what's in the news.
The specific security considerations you might want to consider, if you are included among those whose information was compromised, are general protections against identity theft. That's a broad topic with good advice on this site and elsewhere.
...I don't think you have to worry about threats based on your specific medical history. Firstly, there's no indication detailed medical records were compromised, just subscriber information. Secondly, taking advantage of that sort of thing is somewhat custom - like blackmail - whereas identity theft is relatively wholesale. The attackers are going to cast wide nets with this info, not bait individual hooks.