How to wear a headband after otoplasty?

I use the headband simply as a "reminder" that surgery was done and only have adults wear it when they sleep to protect the ear from being accidently folded. It should NOT be tight as it could interfere with blood flow to some of the skin and cause scarring. Your surgeon is the best person to answer your question

I would say that it is best to ask the question of how to wear your headband after otoplasty with your particular surgeon.  Your surgeon is most familiar with your procedure and would be able to give you the best advice.  In general, usually a headband after otoplasty should not feel tight and should primarily be used on the upper part of the ear.  Your particular procedure may determine any variation to this aftercare, so please check with your surgeon to be sure.  

In general terms it always best to seek advice from your surgeon. Im surprised they have not advised you already.
In general terms bandages don't contribute to the outcome so we usually remove them at 48 hours once the risk of bleeding has diminished. 
I then ask all patients to wear a comfortable headband in bed at night  for 6 weeks. It is just to stop the ear accidentally folding forward. It should not eb too tight. If a headband doesn't cover the whole ear its not a big deal but if you prefer you could wear an elasticated hat.
I also advise kids to wear a head band in the playground for 6 weeks