Hi there - yes, it does sound like popeye disease and it must be treated promptly otherwise the fish will go downhill fairly quickly and perish.
I used MYXAZIN to treat a case of popeye on one of my mollies and it cleared it up very quickly. Can't recommend anything else as I've not used anything but Myxazin for it.
It doesn't harm the filter bacteria so shouldn't affect your fish-in cycling and in the absence of a hospital tank there isn't much choice really as you need to sort that fish out asap - even leaving it a few days untreated can escalate the illness and cause other bacterial problems to occur (eg wasting/fin rot/body rot/rapid breathing etc).
Check your tank stats because a common cause of popeye is elevated levels of ammonia and/or nitrite. As you are doing a fish-in cycle I guess you are doing regular water changes, so do a water change before you start the medications, too.
Anyway, if you can start treatment as soon as possible then the fish might have a chance of survival.
Regards - Athena