I am hypothyroid as well, and had same issue. You can try painting the soles of your feet, if chest is too sensitive, or belly. I also used iodoral tablets. Just try one to make sure you are not allergic. Optimism website has more information.
You would be surprised at how little doctors know about being hypo and getting chest pain. I was given painkillers, hormones which did nothing. I only found out about iodine usage for this condition by searching on the web. Iodine worked immediately on me. No more chest issues!
And then getting on natural thyroid meds helped, Armour and NPThyroid.