My elder sister [5 years older] lost a piece of clothing and then demanded that I search for it with her...?

No, you were right to object but keep in mind how stressed she probably is. Frankly I would have done something a little differently, I would have reminded her that she was cutting into her own exercise time and it would just be better to pick a different article of clothing to wear instead. It's exercise - it really doesn't matter what clothes you wear because you just end up sweating in them anyway and throwing them into the wash. I've never understood why people dress up for a work out. Anyway, the next time she has a hissy like that, just tell her to wear something else and to stop taking her frustrations out on everyone around.