Tooth and jaw ache after deep filling, however it's not sensitive to hot or cold. Could this mean I need a root canal?

Possibly... But your dentist would need to look at the tooth and test it to see if root canal therapy is indicated. Could be from the injection or from keeping your mouth open for a while.
Non-vital tooth? Could be a number of things: body's reaction to a non-vital , necrotic pulp ("dead nerve"), a reaction to the injection of local anesthetic, a disrupted occlusal relationship from the new filling or something entirely unrelated (abscess? Infected impacted tooth?). See your dentist any time an abnormal symptom lasts more than 3 days; asap if there is swelling.