Do I have to adjust my health care coverage if I put that I wasn't covered all year but just found the paper that shows I was covered all year?

[KristinaK]

There is no penalty for not having health insurance on the federal level, so no adjustment/amendment is needed for that. However, depending on the state, if you did not have a full-year coverage, there may be a penalty on your state return's level. So an amendment may be needed to remove the penalty. 

Here are the steps on how to amend your return.