Do I need a filling or root canal for a deep cavity in my molar with spontaneous pain? (Photo)

You need a root canal. The film shows deep decay extending into the distal pulp horn of your pulp chamber (the cavity is in the area of your tooth containing your nerve and blood supply.) Your reporting of your symptoms follows classic progress of decay though the tissues of the tooth. Pain on stimulus that goes away after stimulus is removed is reversible pulpitis, spontaneous pain that lingers is irreversible pulpitis. The pain suddenly dropping a lot is due to necrosis of the tooth. With multi-rooted teeth like this #19, it is possible to have a "dead nerve" and still feel some pain because it's possible that only the nerve in one of your roots is necrotic at this point.  
If i saw that film and you were experiencing no symptoms other than maybe those of reversible pulpitis, I would be conservative like your dentist wants to. He probably is planning on doing a procedure called a pulp cap. I do them all the time and they are very successful. However, once you have spontaneous lingering pain it is time to remove the nerve. Update your doc and tell him your newest symptoms and he will either perform the root canal or refer you to an endodontist. 

Hi:It is difficult to say if you need a root canal for sure. However, most likely the symptoms you are describing could be related to irreversible nerve damage.  It’s best to do another test on the nerve of the tooth.’Best,Dr. Maddahi

I would recommend to get a consultation with an endodontist. He or she can do further testing to determine the best treatment option for the tooth in question. Placing a deep restoration that is in close proximity to the nerve may alsoleave a lot more variables than may need to be readdressed in the future. However,  are many instances when in is acceptable to place deep restorations. All depends on the particular symptoms and situation.