I am a bit confused over this. Someone with heart disease would be in lots of pain if their heart rate jumped to 180+ bpm within 1 minute. My Angina used to kick in between 100-140bpm. Your blood pressure is pretty good too and doesn't seem to reflect problems with artery restrictions. While there is obviously a problem with your heart rate, I would think it more than likely not related to disease. If you do go to the hospital, ensure they run a batch of blood tests to ensure your electrolytes etc are in balance. Any good Cardiologist will do this as a matter of procedure.
Tightness in chest needs to be checked out. Your pulse should not go up to 185. That is over your maximum. You need to be checked out & probably a stress test. Call your cardiologist. If you start having chest pains, go to the ER.