I bought health insurance in 2015 directly with BCBS without going through the state exchange program. When I answer this question under the Health Insurance Tab, it says no further information is needed by the IRS. How then can I claim the premiums and

The Health Insurance/ Obamacare tab is not about Medical Expenses- its about verifying coverage.

This section/ the ACA law is concerned with 2 things-

1/ Did you have Health Insurance?

2/ Did you have health insurance through Marketplace/ Obamacare? If so, enter your 1095-A

If you are a Yes and a No, that would be the end of the Health Insurance tab.

You enter your Medical Expenses under Federal Taxes- Deductions and Credits- Medical