I have an anxiety disorder, for which I take medication and receive counseling. I work as a paralegal in a big law firm. My old supervisor was very organized. We had a weekly meeting to discuss progress on cases, she was very clear on assignments, and she gave me notice well in advance of any meetings I had to attend about cases. (I sometimes have to present information at these meetings, and my anxiety can become overwhelming unless I have plenty of time to prepare.)
Now I have a new supervisor, and it's a disaster. She comes in my office all of the time to talk about different cases and give me assignments. She sometimes springs meetings on me at the last minute, once asking me to pinch hit for a coworker when it wasn't even my case. I've tried to tell her that I need clearer instructions and more time to prepare for meetings, but she just says I need to adjust to her style. My anxiety is getting so much worse; can I ask for a different supervisor?
Often, changes in supervision are the most effective reasonable accommodation for mental disabilities, including anxiety. Notice I said changes in "supervision," not necessarily a change in the person who is doing the supervising. It all depends on how your condition manifests and what changes are possible given your job and your employer.
But first things first: You are entitled to a reasonable accommodation only if your employer is covered by the Americans with Disabilities Act (ADA) and you have a disability as defined by the ADA. Private employers with at least 15 employees are covered, so it sounds like the first requirement is met.
Whether anxiety disorder constitutes a disability depends on how your condition affects you. A disability, as defined by the ADA, is a physical or mental impairment that substantially limits a major life activity (such as sleeping, thinking, or caring for oneself) or a major bodily function. Even if your condition is largely controlled by medication and treatment, it still qualifies as a disability if it is disabling when active, without taking these mitigating measures into account. Garden-variety nerves, such as fear of public speaking -- said to afflict most people -- or first-date jitters are, of course, not disabilities. But an anxiety disorder that puts significant limits on your daily activities is a disability under the ADA.
Assuming your anxiety disorder qualifies as a disability, you are entitled to a reasonable accommodation: changes to your job or your workplace to enable you to perform the essential functions of your position. As noted above, changes in supervisory style -- including giving assignments in a particular way, providing feedback more or less often, minimizing distractions, and so on -- are sometimes very helpful for anxiety disorders and other disabilities. In your situation, for example, you might want your supervisor to give you advance notice of any meetings at which you will have to speak, to provide you with written assignments at the start of each week, to minimize any changes to your work or schedule, and to stop interrupting you when you are trying to get your work done.
Even if you would rather report to someone else, the ADA doesn't give you the right to tell your employer how to run its business or who to promote. You are entitled to an effective reasonable accommodation, not necessarily the precise accommodation you prefer. You and your employer must sit down and discuss the options for accommodating your condition to come up with something that will work for you without creating an undue hardship for your employer.
To get started, write a reasonable accommodation letter that explains your condition and sets out some accommodations that might work. You may need to include information from your doctor about your anxiety (or offer to provide it, on request). For tips on what to include in your letter, see Requesting a Reasonable Accommodation. You can find lots of accommodation ideas at the website of the Job Accommodation Network; look for "anxiety" in their A to Z list of disabilities and accommodations.