Can you detect heart problem from a mere pulse throbing.?

Sometimes. If the pulse is unusually slow, unusually fast, and/or irregular, one can infer a cardiac problem.
More Info.. At your age "throbbing" could indicate conduction abnormalities, ectopic beats, arrythmias, or be nothing. You would be best served by discussing face to face with your doctor who will have a better chance of giving you an answer.