As for what you can do - I would recommend reading the parent accounts on sites like 4thwavenow.com/
There they share how they talked to their kids, what worked, what might not have worked. At the very least it will show you that you're not alone in this, and that this isn't easy for other parents either. There's also various threads here on FWR from mums in the same boat as you.
As for arguing with your child, you need to be the adult here and model good behaviour. (I know that sounds pants, but if you get emotional and agitated, so will the child. They look to you for instinctive guidance on how to react. It's hard to self-regulate your emotions when hormones flood your system. Even harder when mum is getting so angry and exasperated.)
I understand that you're arguing for the most part because you're worried because you know this isn't the solution to your child's problems. But there are better ways to approach it than having big arguments.
My middle DC was very challenging at that age. Still is, but at 18 is now less prone to angry outbursts. At the worst times, I followed the advice in a little parenting book called "Get out of my room but first take me & Alex into town" by Susanne Franks. I also referred to "How to Talk So Teens Will Listen and Listen So Teens Will Talk", that's a book by Adele Faber and Elaine Mazlish. The techniques for finding ways to communicate with your teen when you're in conflict were quite useful to me.
It isn't easy to parent a teen at the best of times, and what you're going through is even more challenging. And in that situation, I like to tap into the wisdom of others. Another book I recommend is "Blame My Brain: the Amazing Teenage Brain Revealed" by Nicola Morgan. It explains a lot of stuff about my teens' behaviour that I found frustrating.
Don't get me wrong - I set boundaries with my kids and one of them is drawing the line firmly on calling me names. No matter what they think I'm doing wrong, I do not accept that kind of behaviour. So when the argument or situation is over where one of the kids overstepped a ground rule, and calm has returned, I call a family meeting and remind the kids of what's acceptable behaviour. And then I spend most of the time listening to them, really taking in what they say, asking questions (not repeating the argument from before. It's mostly about how they feel and what I'm doing wrong
)
If it's properly fraught, we've even done the talking stick (wooden spoon in our case).
But in your situation I would try to wind it all back down to a less confrontational level, one where the kids feel like I'm hearing what they say. It doesn't always work straightaway, sometimes I need several tries. Sometimes I'm too angry to do it, so I tell the kids that I'm going for a walk to calm down. It doesn't hurt them knowing that we can wrestle with strong emotions, too.
I wish you all the best Skatastic and I hope you'll find a way to talk to each other in the love that you clearly have for your child 