It doesn’t sound like anything inappropriate was happening with your brother. Have you asked your parents to tell you specifically what they are uncomfortable with? [name_m]Just[/name_m] hugging, sitting next to each other and so on sounds like really normal brother and sister behavior. While it is true that a thirteen year old boy is going through puberty, that doesn’t mean that he can’t continue to have a close relationship with his sister.
For what it is worth, my brother is four years younger than me and we were always very close. The rest of my family was really not affectionate at all- my parents rarely hugged us and never kissed us. But my brother was just born needing a lot more physical affection and we always had a more affectionate relationship than the rest of the family. It was never weird, even when he was going through puberty. A boy’s sister is just not the focus of his raging hormones!
If they are just telling you that you are being inappropriate, that is pretty vague. I would sit down with them and calmly ask them to explain exactly what they mean. If you feel like they are being unreasonable, see if it is possible to talk with them along with a counselor or pastor or someone similar who can give some perspective. It will help to clear the air. I think that once you have this straightened out with your parents, your relationship with your brother will get back to normal because you won’t all be walking on eggshells.