Sometimes getting a diagnosis no matter what the problem is be it medical or mental, helps because some medications are found to help more with bipolor vs schizophrenia vs depression, anxiety disorders and so on. and some disorders and deseases have some simular symptoms.

Sometimes a prescribing professional has access to therapy files and so on and read them before seeing the client for medication so sometimes they don't ask alot of questions becase they already know the answers. The professional most likely did not ask for your bloodwork paper because there is only a few medications that they use bloodwork to keep track of such as people on lithium have to have bloodwork done periodically to monitor the amounts in their body.

Since you are conserned you might want to seek a second opinion - talk to another psychiatrist or your family physician and they can let you know if the medication and dosage on the prescriptions you just got would interact wrong with each other or is too high or low or is the wrong medication for you.