Why is it that I start shaking whenever I get into a strong argument? My legs shake the most.

? cataplexy. Intense emotion of any kind can prompt a knee-buckling - like your muscles are about to give out. Occasionally it can even involve the neck and head. This can be a symptom of narcolepsy. If you also experience hallucinations upon falling asleep - actually in the twilight before sleep - or upon awakening consider it. Also includes sleep paralysis and nap attacks. Diagnosis - multiple sleep latency.
Anxiety. I believe that the shaking is an emotional response to the arguing. Probably you are raising your blood pressure as well. You should try to calm down. I know that is easier said than done.