There is no barbiturate in either of those medications. Suboxone contains buprenorphine, which can show up as an opiate on some tests, and naloxone, which is not a controlled substance and does not cross react in tests that I have heard of. And zomig is a 'triptan' that has no narcotic or barbiturate in the formulation.
Are you certain that is all you have taken? One common migraine med that WOULD show a barbiturate is fiorinal; another name is 'butalbital'.