Hi jd,
some answers to your questions-

Is there anything between PT and surgery?
Well possibly - long term {lifetime} Bodywork, Posture, ergonomics, learning how to stay away from things that cause flares/pain.

Some cervie ribs are small nubs and some are thick and a full set.
Did you have some sort of neck pain all your life or is it all new from the TOS?

Should I try a chiropractor?
I've had good help from a very good one- but I don't have the extra c ribs.
A full evaluation -with your xrays- by a very good chiro wouldn't hurt- but I wouldn't let them treat you until you are sure you have found a good one.

Does working at a computer all day make this worse?
YES-
Much of the cause is related to the static upperbody postures and fatigue of holding the arms forward and also the head forward. Then the shoulders hunch or roll forward and the c spine curve changes too, all of this causes decreased blood flow, sticky fascia, and compressions.

Are there good career changes if I need to make one - teaching perhaps?
If you are able to - anything that that allows freedom of movement and freedom to adjust to your needs body/use wise.
low stress, no quotas, no continuous heavy or desk work