Hello and welcome to HealingWell.
Patients with hyperthyroidism freqently have symptoms that involve the heart. The most common symptoms are a feeling of palpitations and a sensation of a racing heart beat. These symptoms are due to a physiologic effect of thyroid hormone on the heart.
No it is not unreasonable to ask for that blood test, it is not like asking for a MRI.................... Why make an appointment with your GP when it is your palpitations that are bothering you? Ask again for your test.