According to Naver dictionary, "결리다" means:
숨을 크게 쉬거나 몸을 움직일 때에, 몸의 어떤 부분이 뜨끔뜨끔 아프거나 뻐근한 느낌이 들다.
I think it's a sudden deep pain that makes it hard for you to move a part of your body. Personally, I sometimes had it when I was a boy - after sudden sprinting sometimes you'd feel a stabbing pain just beneath your ribs to the side, so much that you could barely walk - I would say "옆구리가 결린다".
This article might be helpful:
고개를 숙인 자세로 오래 일한 후 어깨 근육에 담이 결렸다고 병원을 찾아오는 분들이 많습니다. 근육이 딱딱하게 뭉쳐지면서 통증을 유발하는 근막통증후군이 아닌가 싶어 근육을 풀어주는 침 주사도 여러 번 맞아봤지만, 그 효과가 오래 가지는 않는다고 합니다.
On the other hand, "쑤시다" is much more generic - the verb originally means "to poke" and move around - e.g., imagine picking your nose, or kids poking a heap of leaves with sticks. It can mean a dull stabbing pain, or even generic muscle pain or arthritis. If it's a more acute(?) sense of pain (like poking with a needle), people may say "찌르는 것처럼 아파요."
Disclaimer: I'm not a doctor. Please don't take these as medical definition. :P