I've been taking thyroxine for 9 years since having a thyroidectomy for thyroid cancer. I've never felt totally well on it and the doctors and endoctinologist are useless. All they do is alter the dose or add some T3 which doesn't help. But for the past couple of months I've been feeling so ill with symptoms of hyper and hypo at the same time. For example I have hyper symptoms like rapid pulse and sweating and it was so bad that I stopped taking the thyroxine totally for a week and am now taking a low dose (against doctors orders) but although it's made me very tired and apathetic, my heart rate is still too fast. I am seeing the endocrinologist again tomorrow but he is completely useless. I know he will do nothing. Even though he is unable to make me feel better he keeps on discharging me so that I have to go through my GP again and wait ages for another appointment. I feel so ill that I am going to kill myself if he does nothing to help me again.
Insist with your GP on a second opinion. Tell him/her exactly how you feel. As for your other question, yes one can have both, it is because of fluctuations.