Car is a 5 speed. When I start driving in 2nd and 3rd and 4th gear around 2000 rpm the car sputters just till like 3500. No engine codes. I noticed the vacuum jumps around d from being negative vacuum positive pressure. Is that causing my issue?

When I'm driving in 3rd or 4th gear and the speed is accelerating, the car bucks and jerks. And it does the same if in low gear and the rpms go under 2000. Mainly in 2nd gear. I know I have bad oxygen sensor and catalytic converter.