If my parent pays for my medical premiums, do I check the box that says "I shared this policy with another taxpayer who's not on my taxes"?

If you received Form 1095-A in your name, you would not check the box indicating that the policy was shared. 

However, if you did not receive your own 1095-A and your parents are not claiming you as a dependent, you do need to check the box.

If your parents did NOT tell the Healthcare Marketplace (usually when they applied for health insurance) that you were not going to be their dependent, you will NOT receive a 1095-A of your own.

• You will need to get a copy of your parents' 1095-A and enter it on your tax return.  On the screen after entering the 1095-A, you will check the box indicating that the policy was shared by somebody that is not on your tax return.  It will then prompt you with further questions to determine how much of it is "allocated" to you (even if it is 0%). Your parents would follow this same procedure.
• If there was Advance credit received (column C of the 1095-A), your parents have the option to claim 100% of the 1095-A on their tax return, or to "allocate" part (or all) of it to you.  If you both agree, the allocation can be anywhere from 0% to 100%.  If you cannot agree, then the Advanced Credit amount is divided by the number of people on the insurance policy.  For example, if the insurance policy covers 4 people, each person is allocated 25%.