Hello and thank you for the detailed description of the problem.
When you mentioned "cilia" you basically gave me the information I need to know.
The fish had a parasite attached to it that although it appeared to fall off could have still penetrated the fish and yes could definitely affect and spread to the rest of the fish.
Before discussing a treatment plan I'd like to mention that the 2 major causes of fish disease are poor water quality and the addition of new fish to the tank who bring with them disease.
Poor water quality usually occurs as a result of lack of sufficient partial water changes, overfeeding and overcrowding. 25% of the tank water should be changed once a week.
The fish should only be fed a small pinch of food once or twice a day and there should be tank large enough to comfortably house all the fish.
New additions (new fish) should be quarantined for at least 2 weeks and observed for diseases before admitting to the main tank.
So please keep in mind these basic tank maintainance procedures.
As for treating the fish. Neons are very sensitive fish and medicating them should be done with extreme caution. The medicine I am recommending be used for this problem is called Malachite Green, click on link below for a view of the product.
Malachite Green is available for purchase at most pet stores where tropical fish are sold. To use, just follow the directions on the product label but as I mentioned Neons are quite sensitive any overdosing could kill the fish.
Caution: If anyone suggest that adding any kind of salt to the water is helpful, disregard the advice as Neons do not take kindly to salt in their water. Salts, especially aquarium salt are generally helpful in combatting parasites but with Neons it is not advisable for the reason mentioned prior.
Best wishes and please let me know if you have any questions.
http://www.drsfostersmith.com/product/prod_display.cfm?c=3578+4615+4616+4745&pcatid=4745
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YOUR TROPICAL FISH RESOURCE
OVER 20 YEARS EXPERIENCE W/TROPICAL FISH---BREEDING, MAINTAINING, CURING
Hi again and thank you very much for your accept, bonus and kind feedback.
You mentioned something in your feedback which pertained to cleaning the tank.
If you meant changing all of the water please do not do so as this will cause problems down the road. Changing 25% of the water is fine. Just wanted to make sure and touch base with you on this.
Take care.
Whew!--I'm glad you're aware of it.
Thanks for letting me know and best wishes on a healthy and thriving aquarium.