I have had the extremely tight chest, too, for years, off and on, and I can assure you, it was, and it is anxiety. (for me ... and sounds like for you as well) It did start after my diagnosis of hypothyroid, but I do know, (now) that I always had anxiety issues ever since my childhood. It just grew out of control after having health problems, mainly while I was my sickest during my worst yeats, (of trying to get levels corrected, and get well)
At that time I just came hyper vilgilent over every little symptom, thus, extreme worry and stress, which caused the tight chest. (I think at times I even concentrated too much on my breathing, ... every breath I took)
My levels are not in a bad range, today, (after 10 years on treatment), I feel pretty darn well, ... finally. I do still have days of anxiety, but no longer think it's caused by my thyroid. I know I just worry and stress too much about things. If I get angry, upset, worried ... my chest gets tight. It has been so tight, I've had to remove my bra, even. (it felt like is was strangling me)
My (mental health) Dr. tells me that this is a VERY common symptom of anxiety. I know it IS anxiety, as when I take a Klonopin, within 45 minutes to an hour, it goes away, completely. I try to only take them when I really need them, which is not very often these days, fortunately.
Yes, I think the other poster is right on target, about a small increase.. Try a small increase, and bring your Free T4 and your FreeT 3 up a bit. Then see how you feel. If you continue to get the tight chest, I would ask for something for that. Talk to your Dr. about it. Anxiety can make a person have all types of symptoms, too.
I also get the tight chest, if I become the slightest bit hyper. And stress or worries, or upsets, seems to go straight to my chest!!
(I'd rather it be something else) Nothing feels worse to me than not being able to breathe, properly, and feeling as if I have a dry cleaning bag, tied over my head.
My best wishes to you.