One day I was brushing my theeth and when I turn my bathroom faucets broke and I went to home depot but they told me that I have to replace all my faucets set, but I was wondering if anybody know if I could only replace the screw that is broken inside the handle,please help

Is this a single or two handled faucet? If a one handled and the cartridge has a stem the handle attaches to then replace the cartridge and install the old handle on that. If a two handled valve then replace the stem and washer assembly. Good luck, tom

Was it just the handle that broke or did the stem break?