When I swallow my left ear hurts and my left soft palate is sore. Why is this?

Could be TMJ . If you clench or grind your teeth, the tmj, which is close to your ear, as well as the muscles of the soft palate can get inflammed and cause these symptoms.
Ear ache. You could have an ear infection, so the eustachian tube (a canal that links the ear to the pharynx) is inflamed and affects the pharynx and palate. Thus, when you swallow the movement of the pharynx and eustachian tube causes pain from there into the ear. A sore throat can have the same effect, reverse direction. Get checked by your physician.
Many reasons. Yes, it could be associated with ear infection. However, other sources could be from tonsils getting inflamed, an ulceration or lesion on palate or throat, and infected wisdom tooth in area. If it does not resolve shortly, i would first seek help from your family physician. Then seek dentist's evaluation.