It could very well be mucus around your stools. This happens because the bowel will create mucus when you are heavily constipated to make the stools slipperly so that they move out - so don't be scared of the mucus. Don't jump to the conclusion they are round worm "nests". I've had mucus around stools myself, and it was definitely mucus from long term constipation.
A good supplement to add for constipation is potassium. Potassium assists/restores peristalsis.
If you do have round worms; it's best only to treat yourself if you actually see a worm... the medicines to use are either mebendazole or pyrantel palmoate.
Good luck and try not to freak... I do think what you are seeing is mucus.