Hi L.,
I was first diagnosed with hypothyroidism during my second pregnancy (with my now 11 y.o.) and have been on medication ever since. I've never had any side effects. My initial symptoms were loss of hair, feeling cold all of the time, and absolute mind-numbing exhaustion. I would sit on the couch and just stare.
With medication, I have a normal balance of hormone, which is checked about once each year with a blood test. I have had to increase my medication a couple of times and each time have had a recurrence of the original low energy symptoms prior to the increase. It's not that being on the medication means that you'll be on medication for the rest of your life, it's that needing medication means that you'll probably need medication for the rest of your life because once your thyroid stops working as effectively, it rarely starts working again. My dose went down after my pregnancy, but has gone up since. It takes time for the medication to balance out, which is why they have to wait a few weeks to see how your body is responding to it. The rechecks also let you know if you need to reduce your medication. For my last increase, my T4 was actually just at the bottom of the normal range, but I was fatigued and symptomatic. When the doctor increased my dose, my T4 went right into the middle of the range and my mood and energy came back up! That is evidence that I'm on the right dose at this point.
Your thyroid is a really important gland that controls many of your metabolic functions. If it isn't working right, your body can't perform normally. At the extreme, you can go into coma (although your numbers are nowhere near that). The medication, whether the "natural" hormone or the synthetic, replaces the thyroid hormone that your own thyroid is unable to produce on its own. TSH is Thyroid Stimulating Hormone and it goes up when your body isn't making enough thyroid hormone (e.g. T4) as your body struggles to tell itself that you need more thyroid hormone. Your T4 is low, which means that your body is not making enough T4. Why your TSH would have gone back down is a question that you'd need to ask your endocrinologist, but the low T4 is what is treated, not the high TSH. The TSH measure is more of a screening, I think. I know that they did not start me on medication until they'd completed a more thorough screening of my hormones.
Good luck! You are definitely not alone: I've heard that 20% of women are hypothyroid. Oddly, my brother is also hypothyroid, although it's much rarer in men, and he had horrible symptoms prior to proper treatment.