I have been getting headaches with mild pulsation on the right side of my head. Why is that so?

Headaches. Your headaches could be coming from tension, eye strain, tooth grinding, dehydration, lack of sleep/poor sleep, skipping meals, stress, sleep apnea/snoring, or chronic sinus problems.
See a doctor. You may be suffering from a type of tension headache or a more serious condition called temporal arteritis. You need to see a doctor asap for more workup including labs. If it is termporal arteritis, seriousl complications can occur so you don't want to put it off.