My two are always bugging each other too. I've found that I make myself more crazy about it than they drive each other. I've resorted to "hugging time". If they treat each other badly I have them hug for a minute, maybe even a little kiss to go with it. I remind them that they are Brother and Sister and Best Friends too. (hugging time lasts for 30 seconds to a minute, so just a bit longer than a natural hug would last)
Sometimes they get "together time" if they bicker. They are made to play together in the same room, UNsupervised. They have to work it out together without me, and can't come out of the playroom until they are playing nicely together. At 4 and 5 they understand exactly what the point of these excercises is. Learning to work it out with siblings prepares us to work it out with friends, classmates, neighbors etc...
I also remind them that nobody likes to be around fighting, so that is why they are isolated, and NEVER REFEREED. Your a Mom not a ref. Deciding who is in the wrong and who is in the right in a fight doesn't help to end the fighting, it brings you into it. Even if one child is at fault make them figure it out.
Discuss your feelings with the instigator in a quiet one on one "meeting" after they have had time to work on it independant from you.
If consiquences are in order for hair pulling, pushing ie: hurting another person - remove posessions. Start with their very favorite item and take it away for a period of time (1-2 whole days). Put it on a high shelf in plain sight (the top of the frig). If that doesn't work, start giving items to the goodwill. "There are lots of kids that are NOT hurting others that would like to have that item." It sounds extreme, but if you want the fighting to dwindle quickly, it works. It might be hard for you to give stuff away, but you'll get over it as soon as you see how it changes their attitude. It has to be something they treasure, but not their favorite item when it's given away FOREVER. Do it one time and they'll be careful not to test you on that one. A threat of a trip to the goodwill and they'll shape up after it happens once. If you end up going down this path, they have to go with you for the drop off of the item so they witness the item being left behind. FOREVER
Call a family meeting to outline how "picking" at eachother will be handled going forward. Then they know you will no longer allow this behavior or participate in it. Family meeting should be handled like a work meeting. You're the boss you lead the meeting, tell them how it it, and answer questions. Everyone should be present - dad, mom, kids and even baby.
Bickering gets isolation together
Hitting/hair pulling gets loss of posession either temporary or permanent