I am so sorry that you are dealing with this constant fighting of your thyroid. This is actually not very common according to research although it appears that the symptoms or side effects (such as heart palpitations, depression, etc) can be treated with prescription medications such as anxiety pills and beta blockers for heart palpitations.
It appears that exercise, yoga and breathing techniques have been a common thing that people have done to try and control their palpitations although as you explained, you are not suffering from that right now. My best advice to you would to try and get a second opinion since this is not a common disorder and try to find a doctor who is well versed in the juggling thyroid issues. Can you keep us posted?