Ditto to Kimberly's and Liz's comments. When I was diagnosed, it was because I went to my GP to get a new metoprolol (BP med) prescription and I finally, after a year of experiencing tremors, reported them to my doctor. My GP said that metoprolol would help with the tremors, and after my blood test confirmed that I was hyperthyroid, she doubled my dose. (After I mentioned the tremors, she noticed that I also had a goiter, eyelid retraction and had lost 75 lbs, so my diagnosis was pretty obvious). We reduced my metroprolol to my previous dose after I became euthyroid.
Just to confirm - the medication you're on now is methimazole? That's too bad that you didn't have a good outcome from the RAI. I eventually had a successful TT, but it actually took me an entire year to find the right dose of methimazole. I was an unusual case, though. I became very hypo for a while. I think there must have been a change in my antibodies, but they were never tested so I can't say for sure - it's just the only explanation I can think of.
Oddly enough, I've been having heart palpitations lately that are worse than the ones I had when I was hyperthryoid - and I just recently had my second best thyroid lab ever - only my second normal TSH since I was diagnosed in 2011. I wear a fitbit and, even though I can feel my heart beating strongly in my chest, my BP meds keep my resting heart rate in the 40's. The other day I was having heart palpitations as I was lying down for a nap. I decided to check my BP and it was 100/65.
Anyway, the point I'm making is that, for me anyway, heart palpitations aren't a matter of my heart working too hard - they're a matter of my body being extra sensitive and feeling my heart beating. It's scary, but my technological devices (fitbit, BP monitor) reassure me that I'm really just fine. If you have access to a BP monitor and/or fitbit, it may be good for your peace of mind.