The -아서/어서 clause supplies the experience you went through and 느끼다 reports the sensation or realisation that came out of it: 중국 가서 느낀 거 (what I noticed after going to China), 다 먹고나서 느껴지는 무게감 (the heaviness you feel afterwards). Several lines use it inside fixed phrases — ~을 통해서 느끼다 (feel it through ~) and ~에 비해서 (compared to ~). The passive 느껴지다 shows up too, meaning the feeling arrives on its own rather than being sought.