Hi A.,
Unfortunately, siblings that fight is a normal part of life. I know that doesn't help you right now, but know that it does ease up as they get older. My son and daughter who were 3 years apart fought so much it would bring me to tears sometimes. I would tell them that I loved them both so much and it hurt me to see them treat each other with so much disrespect.
As adults, they are very close and it is hard to believe they ever fought like they did. It eased up in their teen years and gradually faded, but in the meantime there are a few things you can do.
Any time you put multiple people into the same household and living situation, you will have conflicts, it is only natural. Even adults cannot cohabitate without getting on each others nerves after prolonged periods, why would children be any different? Everyone has their own individuality and we expect young children to be better at it than adults? It took me taking a child psychology class for me to get this.
First, you need to give them their own space. I know it is easier to group everything they do into one because it makes it easier on you, but they need their own space and time to themselves. Do they have their own rooms? If not, give them their own part of the room. Do they share toys? It makes sense that they do, for practical and financial reasons but it is important that at this age, they do not have to share too much with each other. Sharing IS an important part of growing up and important for their development. However, for sibling rivalry, it is just as important that they have things/time and space of their own.
Try to make special time for each of them, as hard as that may sound. It just seems practical that they do everything together, but that is actually part of the problem in that they do too much together, and that only intensifies the fighting. Let them miss doing things together so it becomes special. Maybe Dad can take one for an activity and you take the other for a different activity. Then switch on different days. Let them ask, why can't we both do "????" together?" Or let them wonder why one of them is doing one thing and the other doing another. You answer with "because you fight too much the other way, so we are trying this". Let them have a chance to miss what they are taking for granted. (having a built in best friend in each other)
Also, it is important that they form their own interests and hobbies, Don't assume that because one likes to color or draw, the other likes to, etc.... Let them each try different things/activities.
Another thing that people are guilty of and I have also done this, is to assume that siblings close in age like to wear the same thing, have the same toys, etc... Family and friends probably buy them the same things, so maybe you could suggest different gifts for them.
On the other hand, this will naturally bring up the issue of them wanting what each other has. What you do in that situation is to teach them that the only way that can happen is if they learn to share and play nice with each other. When that fails, they need to go back to their "own" things.
From experience, I know this isn't easy and telling you that it does get better is no consolation right now.
Lots of patience, understanding and giving them their own space is my best advice.
Good Luck!