I started buying eyeglasses at VisionWorks. In the process, I learned how to size eyeglasses.  It sounds to me like you may need a frame with a smaller (narrower) bridge.  Look at the bridge measurement on your current glasses. If/When you go to buy new frames, look for frames with a smaller/narrower bridge.

The other thing that I have done.... I've started using nose pads on my eyeglasses. I buy a soft foam nosepad. It has an adhesive that sticks to the eyeglasses.  I have to replace them every couple of weeks, as they collect sweat and then they don't want to stay in place. At one point, my eye doctor sold me a set of hard plastic nosepads.  I didn't like them as they tended to rub my nose.  So, I am back to using these soft foam nosepads.