About 6 mnths ago one molar cracked and formed a hole..painless at first not when it reacts to cold my entire left side throbs..cavity or root canal?

Hopefully....: .... you will be able to save the tooth. Over the past six months the tooth has continually decayed, and together with the fracture it may now be hopeless. Please see a dentist to have it evaluated and treated.

Root Canal Likely: Hopefully the tooth is fixable from a structural standpoint. The pain you are having strongly indicates a need for root canal treatment (or extraction if you can't do the root canal for any reason.) Lingering(more than a few seconds) or spontaneous pain in a tooth that is caused by decay are hallmark signs of an irreversibly damaged nerve that needs root canal or extraction to solve the problem.

Dental pulpitis: Sharp, throbbing tooth pain produced by exposure to cold is frequently diagnosed with dental pulpitis. There are only 2 treatments for this condition: root canal or tooth extraction. See your dentist ASAP.