Back off and let the other person have some space. If you are constantly together, you will continue to fight. If, however, you keep a distance, you’ll soon forget why you were so angry in the first place.
My brother once did something that upset me, and immediately afterwards said, “I’m sorry I did that to you yesterday.” Confused, I said, “What?” and he responded, “Yeah, we should pretend it happened yesterday so you won’t be mad at me anymore.”
Strong familial relationships can withstand fighting. Sibling rivalry is normal; the trick is to keep it contained to small quibbles and not let it blow up into an ongoing, festering grudge.