The appearance of hypothyroidism after radioiodine is a very common complication of the treatment as it is a natural consequence of the disease which is accelerated by the treatment. This may occur as early as two months after treatment or as late as twenty or thirty years.
This fatigue, can be a sign that your hypothyroidism is undertreated. Laboratory references for normal thyroid hormones level doesn't mean that you gonna feel fine.
Every person has his own range of hormones that is normal for him/her (this need to be achieved with consulting your endocrinologist).
Are you getting enough sleep?

Thank you for your post. I'm taking as high of a dose of Armour Thyroid as I can tolerate without palpitations at alternating 3 to 4 grains every other day. I'm not getting enough sleep because I have difficulty falling asleep. I recently began taking 20mg of Melatonin and that is beginning to help a little bit. My new GP (I moved from the UK to the USA) won't prescribe me a sleeping aid and non-prescription sleep aids do not work for me.

I forgot to mention before I'm a metastatic mixed papillary/follicular thyroid cancer patient that had a total thyroidectomy in 2 surgeries. I was told that I was given double the dose of Radioiodine due to metastasis. I haven't been the same since RAI treatment. I still test positive for cancer, but it isn't high enough for another RAI treatment at this time. I've been pursuing alternative cancer treatments. My immune system is depressed, but I'm working on it. The fatigue is what is really holding me back.

When the thyroid gland is under-active (hypothyroidism), metabolism might slow down so that the body does not burn food fast enough to provide adequate energy. So, you may feel fatigue, a daily lack of energy, an unusual or excessive whole-body tiredness not relieved by sleep or rest.

One of the most common side effects of cancer and its treatment is cancer-related fatigue. It is not predictable by tumor type, treatment, or stage of illness, it comes on suddenly, does not result from activity or exertion, often described as "paralyzing" and it might continue even after treatment is complete.
Radio therapy can cause fatigue that increases over time. Usually lasts from three to four weeks after treatment stops but can continue for up to two to three months.

My fatigue has been constant since February 2007. My RAI treatment was in October 2006. I've been experimenting with 4Life Transfer Factors Plus and that has brought on some improvement. I can get things done in short bursts. If I push myself to be really active, then I backtrack pretty bad. But, I'm pushing on very slowly. I'm still struggling with my immune system, but it's improving slowly. The only things that have help have been naturopathic solutions, so far. I had a new Thyroid Cancer Mass found in May, but the blood supply was dead. I had just finished a month of High pH therapy in April. So, I'm pleased about that.