I had a thyroid problem last year and after many tests i have actually found the problem to be Adrenal Exhaustion and the underactive thyroid was a side effect of this. This was diagnosed by my kinesiologist as this is not recognised by many doctors. Adrenals play such an important role that when they become fatigued, many other bodily functions including the thyroid can become affected. I believe the thyroid actually slows down to conserve energy when the eadrenals are not functioning properly. There is a really good book called 'Adrenal Fatigue' by James L Wilson. This helps you understand if you may have Adrenal Fatigue and what you can do about it. I highly recomend this book as it affects many many people who go undiagnosed but then get treated by doctors for other related symptoms and the cause is never addressed. I would recommend you see a professional though.
Personally i prefer to take a more holistic approach as i find doctors to be tunnel visioned and if you don't fit in one of their 'boxes', they don't know what to do so are reluctant to diagnose!
I am also a great believer in proper nutrition being a great mediine against most illnesses and Patrick Holford has some great books to help with this, although he can tend to over do the suppliments.
Good luck in finding out the real cause of your underactive thyroid and take caution if offered thyroxine by your doctor!