Hit a speed bump going about 15 mph, 98 chevy cavalier..Now car will not move or shift to any gear.

You may have bumped the transmission shifting mechanism. You may be in two gears so the transmission will not work. Your best bet is to have it towed to a transmission shop and have them check the shift linkage. Now when you said it jerked when you turned, do you mean it pulled drastically to one side or the other, or your car surged? You also may have broken a drive axle. The transmission shop should be able to analyze that. I'd say it sounds more like a drive-train issue instead of a transmission problem. Since it is a front wheel drive, and it is a 1998 Chevy Cavalier, ( Car age and length of use, not knowing your maintenance of the car.) your more that likely needing an axle repair.

Could be a broken engine mount, and that allowed the engine/transmission to move. Could be a broken frame that allowed the same movement. Have it towed to a reputable shop and diagnosed properly. There are too many variables for us to give any sort of decent guess as to cause or cost of repair.