Need help finding a better camera than my Olympus Zoom.

I currently use an Olympus Zoom (115?) film camera to take my film photos. The one problem I have with the camera is that whenever I turn off the flash, it does long exposure and produces blurry images. This is very annoying since whenever I try to shoot at night, or any conditions for the matter with the flash off, it produces a blurry image (even in broad daylight at times.) I was hoping someone could help me look for a beginner and cheaper camera, that would let me shoot at a higher shutter speed with the flash off. If needed, feel free to personal message me. Any help is appreciated!

I posted some pictures taken by me that show what I am talking about.