I have severe headaches on my right side?

Possible migraine. Headaches that occur on one side of the head are often migraines. These can be throbbing headaches, associated with nausea, sensitivity to bright light or loud noises, and occasionally flashing lights and visual changes. If this describes your headache, try taking an NSAID (ie. Ibuprofen) as soon as the headache starts to abort it before it gets worse. If this is a frequent problem, see an md.
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.