Hypo and hyper symptoms do overlap. The fact that you are cold and have cold hands and feet and are loosing hair and feel anxious makes me think you are hypo, but that TSH result is not hypo. The TSH only responds to hypothyroidism in primary hypothyroidism. Central hypothyroidism can be caused by a pituitary problem and the TSH won't respond properly.
You definitely need more testing. You need a full thyroid panel taking to include TSH, free T4, free T3 and all the thyroid antibodies. But I'm not sure you will get that from your GP. You can go back and ask though. Tell them you just don't feel well and have hypo and possibly hyper symptoms at the same time and need further investigation. If they refuse, ask to be referred to an endocrinologist for help. If they refuse that too you will have no option other than to get some blood tests done privately.
I too used to get that jolting awake in the early hours, the anxiety was awful, the pounding heart and pulse in the ears. All horrible and all either hypo or menopausal for me. I'm a work in progress on both.