Hair algae (and that's what it looks like)does not cause ich. Ich is a ubiquitous protozoan, hair algae is a plant. The Florida (American)flag fish is said to eat hair algae.
Quarantine for a week is considered about 3 weeks too short, but..
if ich is already in your tank, quarantine won't matter.
If you vacuum the substrate every couple days, and replace the old water with new, this will go a long way to removing the nitrates and other nutrients the hair algae thrives on, and help remove ich cysts lying dormant in the substrate.