Why would my doctor refer me to a cardiologist? Is there something going on with my heart?

Talk is best. You really should ask your doctor why he/she has recommended this. The best patient outcomes happen when the doctor and the patient have a conversation and both understand what is going on and what the plan is.
Do not know. I do not have enough info to say why you were refer to cardio. I suspect you are hyperthyroid and that's the reason you were prescribed methimazole. Symptoms you mention can be cause by hyperthyroid state. Any other risk factors for heart disease? Talk to your doctor. Ask him why the consult. Don't be afraid of asking questions. Doctors love it.