Going to work can be painful, having a relationship can be painful, building friendships can be painful, having and losing a pet can be painful, running can be painful. Everything we do of value in life, of any value, can hurt in some way but also gives you the greatest rewards.
Running and yes the pain gives you a sense of achievement and in life what is worth doing which does not involve some discomfort along the way?
When I run up a hill over the south west coast path, I feel the pain, but once I get to the top, looking along the coastline, wind in my face, stunning views, and feel alive at my accomplishment, it makes it all worthwhile.
Pain and happiness are not always mutually exclusive, sometimes you have to suffer the former to experience the latter.