Sorry, not sure about the reverse osmosis or distilled water.
The ick parasite will attack fish that are stressed, especially if the water conditions are not ideal.
I don't know that I agree with Joy about losing the cycle with a full
water change, as most of the beneficial bacteria lives in the filter, filter media and gravel. As long as they stay wet and warm, you shouldn't lose that much bacteria.
However, You should be doing weekly water changes, not monthly.
When battling ick you should do a daily water change of about 20-25%...someone correct me on this if it is wrong.
The best
test kit is the
API master kit, it can be costly, but well worth the reliablity. I think a member found it least expensive at Walmart. Don't use the strips, they are not accurate.
Good luck, let us know how you are doing.