You may have gotten to the vet by now, but it does sound like round worm. Both of my cats were rescues and were strays, so they both had it when i adopted them (at different times). And if the cats share the same box, they will both need to be treated...although you dont need to bring in samples of both...they will just opt to treat all the cats in the hosue...and the litter will need to be changed constantly to avoid reinfestation...and yes, i believe a swollen belly is a sign.

The fierst time i brought my cats to the vet, it didnt show up (just a different intestinal parasite)...but when i brought back a fecal sample to make sure that the parasite went away, it ended up showing the round worm...you cant see it in the feces in its egg stage...only when it is mature...so they may have missed it in a previous sample...