Yes thyroid can vacilate between hyper and hypo. This often occurs in someone in the earlier stages of Hashimoto's. It can also occur from "leaking" nodules on the thyroid. Where every once and awhile the nodule will produce or "leak" out periodically some hormone which causes you to go Hyper.
Please post the lab results you get along with the reference ranges. To be thorough, you must get more than just TSH tested. And finally just being "somewhere" in the normal range does NOT make you "normal" or fine.
To be complete you really need to be tested for both FREE T4 and FREE T3 hormones in addition to TSH.
The fact that you are swinging between hyper and hypo symptoms I would also recommend getting tested for the antibodies for Hashimto's these are TPOab and TGab. Additionally get tested for Graves disease which is the TSI test.
DEMAND that at least the two "free" hormones be tested. This test counts only the hormone molecules that remain unattached to a protein. Therefore they are "free". Once a protein attaches, the hormone is useless and con not be used by your body.
Most people report that then need to be well up into the normal ranges in order to feel well. In fact the better target seems to be the Free T4 to be in the MIDDLE of the range if not slightly higher AND (that means in addition to) their Free T3 to be in the UPPER 1/3 of the range. Simply being at the bottom of the range is NOT sufficient for many if not most people! Do not be talked into being told you are fine when you have symptoms and you are at the bottom parts of the range.
If the Dr is unwilling to test for both Free hormones. I would recommend you find another Dr. Using TSH alone will almost assuredly keep you feeling sick.
HI friend, don't give up hope. I went through 5 yrs of being everything is normal, after numerous test, including ultrasound, biopsy & RAI,. It all began with pressure feeling in the throat. I have lot's of symptoms, but severe fatigue was the worst, I could hardly get out of bed and function.
I had a TT done Feb, 2012,. Still normal labs, only my thyroid grew large enough to take the breathe out of me, after TT I began hormone medication, and amazingly all my symptoms disappeared. It's been 3 months and I still feel wonderful, I don't feel anything like I did before surgery.
As for your questions, the answer is yes to all, thyroid disorder can cause lot's of symptoms. Some experience both hyper/hypo, I experienced both, prior to surgery.
Post up your labs results, when you recieve, someone will be able to assist you. If you have past lab results, post them up as well.
Wishing you well on your journey :)