The friends telling you that your mouse is shit probably mean in relation to a gaming mouse. Before I got my current mouse I was a logitech fanboy 100%, definitely still my favorite non-gaming device brand. That being said, as far as I know there really is no replacement for a decent gaming mouse. I have a piece of garbage redragon M601 and it's still worlds better than any non-gaming mouse I have ever seen.
Now, I may be a noob at OSU but I am fairly experienced when it comes to parents that aren't too fond of gaming. There are a couple of ways to go about this. If you have your own credit card, just let your parents know that there is something wrong with your current mouse and that you want to get a new one, get whatever mouse you want, spend a few days just using it for everything (you will want to anyways), and everyone will forget about it pretty quickly. If anyone does ask just say that a friend has this same type of mouse and that they said "insert generic statement about mouse having a long lifespan/anti-carpal tunnel features/whatever you can come up with".
If your parents are like mine, and don't give you any freedom whatsoever, you will have to be a bit craftier. You kind of have to just say I don't like my current mouse, I want this one. Of course your parents say no, so you wait a day, and repeat. Over and over. Fight for it. Make it clear that a good mouse has many applications other than gaming. Find reviews for the mouse written by people using it for non gaming purposes. Trust me, your parents don't really want to have to keep arguing about it day after day after day.