How do I add a new child to the Mass state return? I figured I'd need to include my child under the health care section since I received a 1099-HC with her name on it

You cannot add your child to the state directly, you must add her under Federal >>> Personal Info >>> Edit dependents to Add a Dependent. State taxes are based on federal taxes, so your information transfers from the federal area, to the state. 

However, you can't start your state, until you have entered everything in the federal side. After you add your daughter, you'll need to remove your state and add it back. To do so: select the State Taxes tab >>> click Continue >>> To the right of your state, click the Delete hyperlink (to the right of the Edit button). Then, you'll be able to Add another state to add it back in.