The symptoms you reported (tingling in right hand, tightness in chest and high blood pressure the other day) might be related to several conditions.
The tingling is primarily a neurologic symptom. Putting pressure on the nerves responsible for the hand might cause tingling. In the case of cervical (neck) spondylosis, the cervical vertebrae put pressure on the nerves that leave the spinal cord in the vicinity. The tingling, in this case, is usually felt along the whole arm all the way to the fingers.
Poor blood supply in advanced cases of atherosclerosis might damage nerves over a long period. Usually one of the first symptoms is tingling because the sensory functions of the nerves are affected sooner than the motor ones.
Advanced atherosclerosis might cause poor oxygen supply in the heart muscle which might, accompanied with high blood pressure, subsequently cause tighness in chest.
You are advised to visit your family doctor for a physical examination. Depending on the results you might be referred to a specialist for heart disorders or to a neurologist. The specialist for heart disorders might need an ECG, Echocardiography, and laboratory tests to determine the condition of the heart.
An x-ray of the spine might confirm cervical spondylosis.