Hi. Could sore gums around my wisdom teeth and a sore jaw cause a sharp pain in the back left side of my head?

Head pain. Sharp head pains in the back of your head are unlikely to be directly caused by those dental problems. They are more likely to be neuralgia which is an irritable/mildly inflamed superficial nerve in the scalp(occipital neuralgia). This tends to resolve without any treatment. More sustained pain can be due to a pinched occipital nerve where it emanates from the neck vertebra from a spur or disc.
Seek treatment. . Yes, you probably have cellulitis which is an infection of the soft tissue. Best to get it checked. The infection could become very serious quickly. .
Not usually. You are describing areas that have different innervation. But as no two people are exactly alike, no two sets of nerves are exactly alike. Your wisdom tooth is telling you you need to see an Oral Surgeon immediately. Once wisdom tooth properly treated, if pains in back of head do not subside see a Neurologist.
Gum, Jan and head. pain. You need to see your dentist or your doctor. Nerve pathways and muscles can be very confusing in the pain they generate and a professional will help you sort it out. Peace and good health.