My fish are getting sick and it happened around the time I added new plants to my aquarium. Could it be that the plants are making them sick?

It could be that the plants you purchased were housed with fish that were sick. If you didn't properly clean the plants before introducing them to the aquarium, you could be passing on a contagious illness.

Plants can possibly carry some sort of pathogen, but the first place I would look is your water quality, have you tested your ammonia, nitrite and nitrate levels, are they in good shape?  Ammonia at 0, nitrite at 0 nitrate below 40 ppm, possily phosphates are out of wack.....  What method of filtration is used?  What is your maintenance practises?  Over feeding?    Fish, like bird's and reptiles,  will hide symptoms for quite a while, it's survival of the fittest in their world.  Once you added plants, it provided a hiding place and possibly the animals began to make their symptoms more obvious...  Also, plants are another living organism and a source of organic waste eg... dead or dieing fronds... increasing the disolved solids in the environment.  Mortality and disease in the aquarium is most times the secondary affect of poor water quality. 
Another thought, what is the temp in the environment?  Many protozoa/parasite manifest in cooler water.  Bacterial infection is usually the secondary affect of water quality.

--------------------------------------------------------------
SOUTHERN ILLINOIS TROPICAL FISH HATCHERY www.sitfh.com