Oh no, not the pretty purple and white one!

Im so sorry to hear that. You had just gotten him too, how sad.
It could have been a bacterial infection which is why it took him so fast. Poor little thing, sometimes theres just nothing you can do for that. The tea tree stuff is Melafix which I personally dont feel has any antibiotic properties. (It heals torn fins though).
I would do a water change and keep a close eye on your other fish. If he starts to show any of the same signs treat with an antibiotic like Maracyn 2. Also your tank is reasonably new right? Any ammonia or nitrite present?