Is my dad being unfair to my sister?

Depends on the real issue. If it's just that he doesn't want to spend money on her, he is being wicked unfair, getting you new shoes for almost no reason and taking you out for fun. If he thinks she will be disappointed if the spikes don't work, and is trying to protect her, it's still not the best way to handle the situation, but at least he's coming from the right place as a parent.