OK, so first of all, let me say it will depend entirely on the whole clinical picture of what's going on for you as to whether you can be truly considered perimenopausal. If fertility is a concern for you, now might be the time to ask for a referral to a specialist, who can do more investigations and give you a more complete picture. Otherwise it's often a case of just riding it out, although as a young woman you can ask for more thorough investigations (eg with a sympathetic gp or a gynae) esp if your periods are on their way out, as there may be other causes of ovarian failure that need to be ruled out. Your Dr should be explaining the reasoning behind not testing the oestrogen levels, so it might be worth finding a good GP who specialises in women's health as your first port of call - because if you are menopausal early it can impact your health in many ways, like bone density, your heart, and sexual function.

Something you should be discussing with your doctor is whether you should be considering hormone therapy of some sort, and if not now, then when? (I have to avoid this because of my breast cancer history). There are arguments for and against, but that by itself could be enough to sort out your symptoms. It's quite important to start looking after your bone density NOW - with weight bearing exercise, calcium/mineral supplements and get your vitamin D levels tested (and take a vit D supplement to boost it). Otherwise there are practical measures you can take - I keep a spritz bottle on my desk and a fan to help with hot flushes. Apparently there's a cooling mat that you can get for your bed that helps if you're having bad night flushes. Dressing in layers (and keeping your bedding light) can help too. There is also an antidepressant that can help with the mood and hot flush issues, but I think that tends to be used by people who can't use hormone therapy for whatever reason.

There are some good websites that talk about early menopause issues:
Early Menopause.org.auAustralasian Menopause Society
Premature Ovarian Failure

Also for an alternative view, get your hands on a copy of Christiane Northrup's book, The Wisdom of Menopause. Not so much about early menopause but lots of good information especially re lifestyle measures and dealing with the mind-body connection aspects.