The short answer, they can test for whatever they want. The State will first test for alcohol because it is the fastest and easiest substance to test for. If the results show that your BAC is below the legal limit then the State will move on to test for other substances.
What they are going to come after you now is that you were intoxicated on prescription meds, or meds combined with the alcohol which caused a synergistic effect. In order for the State to prove up the meds they are going to need to know when you took those meds, what dosage, what the half-life is, and an expert to testify to the effects of this medication with those known values. They will need a Drug Recognition Expert (DRE) to testify about the effects of your medication. So even if your meds show up in the blood, they still need an expert to testify how what showed up was affecting you. This is not easy. An expert can't just come in and compare you to the average person. If they can't make it relevant to you and probative, then the blood test should be suppressed. (this depends greatly on the Judge). They should have had a DRE run a drug recogniton evaluation on you, which would have included: measuring your pulse rate, pupil size, the SFSTs at the station, muscle rigidity, signs of injestion, admissions, etc. It's a very technical 14 step process. There are very few agencies and officers that can get this correct.