If you are seriously doubting you drs diagnosis, remember that you do have the right to seek a second opinion, and its often a very wise thing to do, doctors are usually right, but they are also human and do sometimes make errors.
Copied and pasted from the excellent psych education website by Dr. Phelps . . .
Anxiety can be a symptom of bipolar disorder. This was recognized by the fellow who originally described bipolar disorder as such, Dr. Emil Kraepelin, back in 1921. He described "anxious mania", and also "excited depression", which included a "great restlessness". He specifically named anxiety as one of the components of this illness. All that requires saying, because "anxiety" is not generally regarded as a bipolar symptom. Yet it clearly is, as summarized in an excellent summary by Freeman, Freeman and McElroy.
There are basically two ways you can have anxiety with bipolar disorder. First, it can be a symptom of the bipolar disorder itself. Secondly, you can have a separate anxiety condition in addition to bipolar disorder. In medical lingo, that is called a "co-morbid" condition (in case you run across that term). It means both conditions are present, and thus implies that anxiety is a separate condition, not coming from the bipolar disorder itself.
These two ways of looking at anxiety have substantial implications. If the symptoms are coming from bipolar disorder itself, then they should get better when the bipolar disorder gets better. But if they are coming from a separate condition, they could persist even when the bipolar disorder improves.
If your anxiety is really a separate condition, it's going to require a separate treatment. And that really complicates things, because very often the recommended treatment for the anxiety condition could be an antidepressant medication -- and antidepressant medications can make bipolar disorder worse!