Do you have experience at measuring pulses?
Can you tell me if this is an irregular or regular pulse?
Are you able to measure it?
What is your blood pressure?
How long have you had these sensations on the left side of the neck?
If you are noticing a difference from the right and left side of the neck I would recommend that you ask your family doctor to have a listen for carotid bruit. This is the noise that is made when the blood is slightly turbulent due to narrowing of the artery. This is common in people who have a history of high cholesterol and other circulation problems.
The fact that the pulses are regular is fine as we expect the pulse to beat in time with the heart. Your blood pressure is well controlled so it may be that this strong pulse is normal for you. However I would get it double checked just for peace of mind as a narrowed carotid artery can increase your risk of other problems long term.