Well, there is no such thing as "stress leave" anymore. Everyone has stress and insurance companies therefore do not accept stress as a reason to be away from the workplace.
Your doctor will assess your symptoms and may provide you with a note which will be acceptable for a brief "medical leave". This implies that you have an illness that prevents you from working. It may be depression, anxiety or a sleep disorder but it won't be accepted if it merely states that you are experiencing stress.
Insurance does not cover "workplace issues". For example, if you are being harassed, having problems getting along with your boss or don't like the policies and procedures, asking your doctor for a leave is not going to help in the long run. It is not honest or realistic to expect a doctor to provide you with ongoing documentation so you can be away from work because you just don't like being there. Instead, you may need to talk with Human Resources about how you can resolve the issues.
If, on the other hand, you have a physical problem such as a heart attack, broken limb or addiction, it is totally appropriate to work with your doctor to ensure that you have an accurate diagnosis and treatment plan. Your doctor may refer you to a specialist to help with your recovery and will usually support this by completing the paperwork for your insurance program.
When your problems are because of mental or emotional difficulties such as depression, anxiety or mental illness, your insurance company usually requires that you have assessments and treatment by a psychiatrist and/or psychologist. If the disorder is severe and expected to last for a significant period of time, you may qualify for long-term disability providing the professionals recommend this.
Imagine the letter "T" which is tipped on its side with the top facing the right-hand side of the page. Insurance companies would list workplace issues on the right and expect them to be resolved by Human Resources. Employees with workplace issues do not qualify for medical insurance.
On the top left-hand side of the "T" would be physical problems which need to be documented by a physician or medical specialist in order to justify medical leave.
On the bottom left-hand side of the "T" would be mental or emotional disorders which need to be documented usually by a psychiatrist or psychologist to qualify for medical coverage.
If you are having problems in the workplace, before you run to the doctor for a note to be off work, consider what is really going on.
Stress is not the same as medical leave, and no matter how difficult the workplace issues become it is not appropriate to ask your doctor to give you a note to be away from them. Workplace issues must be dealt with appropriately.
(And, by the way, the employer is likely not going to get rid of your supervisor or manager just because you are upset or stressed or on leave so don't think that being away from your job will result in your wishes being met in that regard).
If you are really ill visit your doctor but if you are unhappy about the job you will need to find another way of dealing with that.