I have a blood clot from a tooth extraction that took place 4 days ago and it is gradually leaving the more I rinse with salt and water as well as I rinse with prescribed chlorexidine. I never got the white residue over the blood clot. So should I worry about dry socket even though I don't have any pain

Nopes, just take care on extraction site is enough.. Only 5% people will be affected by dry sockets.. Not necessary to remove that white coverage.. It may automatically clears off after day 7.. But while brushing,keep care on that area.. You may feel normal aftr day 8th..