You can treat ich without chemicals (but its a pain in the u know what.)
You will need 2 Q Tanks. Fish out everybody and put them in 1 Q tank. Your main tank should remain empty for the next 3 days ( the ich will die because there are no living hosts). Switch fish to clean Q Tank every 8 hours. (By clean I mean - tank should have 100% water changes) Your ich will be gone within 1 week.
Its all in the timing - the life cycle of ich is 12 hrs. Every 8 hrs or so, they drop off the fish and fall to the bottom of the tank to reproduce. Good luck!
As to your neons - I agree they are very delicate fish and kudos to that person who has never had a problem with them - your silver tips may be eating them - neons are universal fish food and should only be kept with the most docile fish (like cories and cardinals)or fish of same size.