It does sound like she is going through that wonderful roller coaster of a ride called Hashimoto's disease. Going hyper means the body is trying to establish a good point of reference, but it doesn't like it, so everything is sped up. The heart doing its little flip flops are natures way of saying, Too much! Left untreated it can cause serious heart damage.
It is best to get it checked anyway as Smilerdeb says, as sometimes it can bring out a previously undiagnosed disorder, Not always, but good to err on the side of caution.
Once her levels are balanced out she will no doubt be fine. Often it is just too much hormone in the body and the body just doesn't like it.
They feel freaky but 9/10 they are nothing insidious, but always get it checked anyway, just to be sure.
Ask your Doc to refer your Daughter for a "heart Ultrasound" to rule out any mitral valve problems as this seems to be common with people who have thyroid issues.
This will also set your mind at ease.
Dont be surprised if there is Mitral Valve regurgitation as I have had it for years and a heart murmur (at birth) which was 'innocent' until my thyroid problems started.
Anyone with a thyroid disorder should have yearly checks with a Cardiologist...its just standard routine.
more than likely its her thyroid levels again.in hashimotos the levels can go up and down over years. they should check her thyroid antibody levels too. could it be her heart? you always have to think of all the possibilities and never blame all symptoms on one diagnosis. have her heart checked out carefully with blood pressure and ekg by her doc, or ask to see a cardiologist if he wont work up these symptoms if her thyroid labs are normal. make sure they are checking a free T3 as well as a free T4 and TSH.