I had a similar problem. I didn't want to wait, so I went to the ER at BAMC.
TriCare has it's issues. It's basically the HillaryCare scam that wasn't accepted by the public, but was rammed down the military's throat.
IIRC, those on TriCare are exempt from ObamaCare. Presently, at least.
Have you tried finding a primary care provider for Tricare? The closest one we could find is 30 minutes away—and he is considering dropping out.