The first breath test an officer will likely ask you to take is a Preliminary Alcohol Screening (P.A.S.) test. Technically this is a field sobriety test, and not a breath test that was initially intended to be used for evidence purposes of a blood alcohol content level. If the officer properly advises you, you will be told by the officer (generally) that the P.A.S. test is just used to determine whether or not there is alcohol in your system, and if arrested you will have to submit to an additional breath or blood test. Even though the P.A.S. test is supposed to be just a field sobriety test, the results are often used against a defendant in pre-trial negotiations, and possibly at trial, if they are the same or higher than the later breath or blood test after arrest (or sometimes if they are just high in general). If you are not already on probation, then it is generally speaking, not a good idea to do the PAS test, or other field sobriety tests. Keep in mind that sometimes they can be beneficial, and there is no 100% sure answer on whether they are helpful or hurtful. Depends on many factors and variables. Also, keep in mind that in some counties they use an E.P.A.S., which can specifically be used for Evidential purposes.
It is also possible to get arrested for a DUI even if there is no alcohol involved, if they believe you are driving under the influence of drugs, including prescription drugs. For example, if the prescription drugs make you drowsy, you can have DUI issues.
If the medication you are taking has only the slightest bit of alcohol in it, it should not creates any issues with either breath machine or blood test as far as alcohol content level is concerned...but of course, there are exceptions to everything. Both breath test and blood tests can have their issues. You can retest a blood sample, so if fermentation occurs that raised the alcohol content, retesting the blood may reveal that. Keep in mind there can be other issues with blood tests.
Likewise, there are some defenses to breath tests that are not as available when challenging a blood test. For example, a breath machine is more likely to give inaccurate results when someone is in the absorption phase (ie. just had a drink immediately before driving). This can be a defense to a breath machine, but not a blood test (although you could still argue rising alcohol content level).
Keep in mind that if you do a blood test, your time at the station after arrest is likely to be higher, since they won't know the results of the blood. If you blow into a machine and the result is .01 (and you are 21 or older and not on probation), you should not have any DUI related issues based on alcohol. If your medicine only has a trace of alcohol in it, and you only take a teaspoon of the medication, I would really be surprised if you had any alcohol related issues even with a breath machine test. If you refuse to do all field sobriety tests (which is generally advisable), expect to get arrested. So you have to weigh in the time factor of getting arrested and then then spending hours in jail after taking a blood test.
This is NOT advise of what you should do, but if I were in a situation where I was 100% fine, had no alcohol or drugs other than a normal dose of cough medicine a few hours ago, and I was not on probation and over 21 years old, I would likely ask the officer to see the P.A.S result if I took it, and if the officer agreed, I would just blow into the P.A.S. test once. If it came back as a .01 or .00 (which is what I would expect based on the above), then I would expect the officer to let me be on my merry way absent some other issue (like a car accident or egregious driving).
Sometimes the officer can go further and think there is a drug issue, and arrest you at that point and give the implied consent speech for a blood test. Remember, NOT advise. There can be issues with any type of test (and defenses to them).