I've used the Family and Medical Leave Act (FMLA) and Short-Term Disability (STD).
My Doctor kept the answers as vague as possible, while still providing the requested information. He felt the details of my illness were none of their business. He listed that my symptoms were still under investigation, affected my ability to perform my job, and I needed the time to work with several medical practitioners in-state and out-of-state -- all true. I knew FMLA would be approved, as it's a legal right. But, two years later, when I applied for STD, I was surprised that I got approved for two months.
I suggest applying for STD first, so you will have income. If it's not approved, for whatever reason, I would try to appeal the decision. If denied again, you could try to go the legal route -- or, just file for FMLA...which will be approved, but is unpaid. With FMLA, in order to maintain your health care coverage (medical, dental, vision), you'll have to continue paying your premiums.