How long has it been since your c-section?
Congratulations on the new baby!
With a c-section you probably need to wait a week or two...but after that you should be able to start short walks. My advice once you can is start going for daily walks! By the end of 6 weeks I was walking miles per day .
Your incision should not continue to hurt. I have had 3 c-sections and was completely healed by the 6-8 week mark. Some times I do get itchy. You should talk to your doctor.
I agree that your incision shouldn't continue to be "very painful" and it definitely shouldn't "kill you" when you jog. I'd call the doctor or nurse if I were you.
Are you breastfeeding? What are your stats (age, height, weight, fitness history)?
The 7 months post op does seem like plenty of time to have been healed. Did you maybe try to do something too soon and developed an incisional hernia? I work for an OB and a surgeon and agree you need to see a doctor- is there a bulge that shouldn't be there?
After seeing a doctor continue the walking but I also would look into some bodyweight exercises. Push ups, planks, squats. lay on floor and use your son as the weight and lift him up over you like a "bench press". Is he crawling? Get on the floor and crawl chase him around the house.