I understand. The tops of arms are often picked as places for self harm due to the fact they can be more easily hidden when required. As others already know about your experiences with self harm i agree that a more suitable excuse for a bandage could avert suspicion.

What accidents could affect the upper arms...i don't know if you have longish hair but maybe you could say you had previously used a heat styler which got caught and slipped out of your hand thereby contacting the tops of your arm on it's way down? There's no need to be as elaborate as that of course, i was just trying to demonstrate the logic. Yes burning is also a method of self harm but i assume not your regular sort? If so that could well be easier to explain away...pay mind to appearances as well as explanations though. The placement of the bandage, for example, is important.

I feel that as long as an excuse is more in line with personal circumstances, the greater the likelihood it will be believed.

I worry with writing stuff like this - i want to provide practical support but not encourage either you or anyone else to become more studious in the art of manipulation. But you state you're aware that a better solution must be found eventually - that gives me greater confidence. If what i've said hasn't been helpful and it spurs you on to a different line of thought altogether - i hope at least its a better one. All the best.