Don't get rid of your mobile phone.
DO NOT run away. You think your problems are bad now? Running away will not solve them, and it may make things 1,000X worse for you. There are adults and even teenagers and people who appear to be friendly or nice, who may try to lure you in since you are vulnerable and running away, and then take advantage of you, sexually abuse you, hurt you physically or psychologically worse than you have ever had happen, or kill you. Stay safe.
In some cases kids are right to run away. Sometimes things really are that bad. I don't know if that's the case here, but sometimes it is.
If you're a minor, while yes, you absolutely 100% want a working phone, but since as a minor there is a risk that your parents, or the cops at their behest rather, could track you with your phone if they know the number. So you might want to get another if that's an option.
Otherwise, while it's in airplane mode it can't be tracked. But if at any time airplane mode is switched off it can be tracked to a rough general area around the cell tower it was connected to.
I'm not going to tell you not to do it. But I will say that being homeless, especially as a minor. It's very, very hard. I'm in no place to tell you that you're better off with your parents. I just hope you appreciate what you're getting in to. There might well be other options beyond doing nothing or running away. And running away and winding up homeless really is an absolute last resort. Doing it as a minor is worse, doing it as a female minor is worse still, doing it as a female minor entirely by yourself is worst of all. It has to be VERY bad at home before running away starts making sense.
Without knowing your circumstances in more detail I can't really say what I think might be your best option. But I want to tell you I'm very sorry you're going through this. I ran away from home, and I've been homeless. But I wasn't a minor at the time. Not by far, but it's still a big difference.
It's a very dangerous thing to do. If you do it, my best advise is to trust your instincts. Never, ever go against them.
Of the most dangerous situations I've gotten into when I've been homeless, most were because I didn't listen to my instincts. Usually out of desperation. But it's just not worth it. Trust your instincts, always.
I'm really sorry you're going through such a difficult time that you feel like you need to run away. Just be careful hun. Winding up homeless usually isn't much better. And pretty much the only time it's any better is when there is severe abuse going on at home. I mean bad enough that you might sooner be dead than stay home.