As the other mother's said you are definitley not alone. While they talked about the logistics of having another baby around I'll address the physical aspects.
I'm a chronic miscarrier. I was thrilled when I started my 2nd pregnancy but I also had the fear of another painfilled pregnancy with a lot of pre-term labor and bed rest. Unfortunately my ex and I had a physical fight and I had a miscarriage. The next 4 pregnancies didn't survive either and each pregnancy produced not only the labor/prelabor fears but concerns for every twitch and pain even between pregnancies.
Then the surprise came, Ds#2 was concieved after I had given up trying. The fears mounted again along with the external pressure of my Ex stopping my visitaions of my oldest for the 2nd time over me replacing his son with another baby. I fell into an anxiety filled pregnancy with nothing to do to fill my time with worry and brood. The labor was just as rough and brought some new surprises. My post-partum was really plagued with depression and anxiety as well. But we made it through.
I concieved again almost immediately but lost the baby and suffered an ectopic before we concieved DS#3. This time my husband told me I needed to have a better mind set. I still had my down days early on but I knew I could do it again because there are so many milestones to look forward to.
You're body will know when it's ready but you also have to let your psyche recover from the trauma. You do have to let go of the letdown of a less than ideal birth. Take advantage of all the modern conviences this next time and you will enjoy it more. No birth is perfect and no birth is exactly like the previous one.
Now all my births were natural, but I know of women that had spiral uterine incisions during c-sections which are more likely to rupture in a subsequent pregnancy and went on to have other children naturally or by c section.
Given your line of work and your education you need to let go of the analytical part of your fears and just devolve into the ripe woman you are and your body will do the rest.
Have fun.