I echo everything dancinggirl said. Also, have you looked at the STRAW guidelines for stages of menopause. That may give you some clarity about your irregular cycles. This looks very early peri to me, and that may be why you're doctor made the comment about not saying your in menopause. It can go on like this for years before you move really transition into menopause. That's not to say you shouldn't be offered treatment for relief of symptoms. The symptoms are real, and some women get them early, some late, for some it goes for years, and some it's very quick.
If you begin missing periods altogether, like 60 day or longer cycles, I would push for FSH testing. They don't like to do it because results can vary, but as DG said, premature menopause is a little different because you need to know. My understanding is that it isn't "natural" to have low estrogen before the typical menopause age, so if you are heading into menopause, the FSH can help determine that. Really the only absolute way to know is if your periods stop altogether for a year, but by then your body will have been already been lacking in that estrogen.