Well 1st of all, since you are the child, and your mom is the parent, it's really your moms job to worry about this kind of thing, not the reverse.
But since you are mature enough to recognize that you do have some responsibility in what is going on, I will try to share with you some of my own experience in this kind of situation.
The trick here is to learn to pick your battles.
Some battles are really not worthy of your time, and you need to recognize the difference between those that are, and those that aren't.
You said you will argue with your mom over little things.
That suggests to me that you (AND YOUR MOM) are a "right fighter".
What I mean is, that once you get the notion in your head that you are right, you will argue with your opponent, until all the rivers run dry before you will give in and say "enough".
You are only 15, so you are in a very important transitional stage in your life. You are becoming an adult, but are still hanging on to some childhood habits. Don't mistake that comment as a criticism. It's human to find it hard to change old habits, and you are hanging on to the childish trait of living life in the moment, instead of looking at the big picture.
Here's an example:
Have you recently found yourself arguing with your mom about you going out to hang with some friends like it's the last time you will ever get to see them ever again?
The truth is, that tomorrow is another day, and you will probably see them then, but when you are not seeing the big picture, and only living in the moment, it seems pretty hard to understand.
I think you are smart enough to figure out the difference between a fight that is worth it, and one that can wait, so I will leave it up to you fro here.