It sounds as if you have several, unrelated problems.
First, if your coolant sensor says you're low on coolant but you're not, then the sensor is bad or clogged up with debris. (These sensors often fail on high mileage vehicles)
If you were low on oil, but then filled it to proper capacity, then the oil level sensor may have to be reset. You'll have to consult your owners manual for that. But it is possible that the sensor has failed also. (Less likely than the coolant sensor)
As far as you car jerking and pulling slow when you accelerate, that would be a transmission issue. The coolant and oil level sensors would have absolutely nothing to do with that.
First check the fluid to see if it's at the proper level. (Make sure the engine is at full operating temperature. With your foot on the brakes, cycle the transmission through P.R.N.D.1.2. And then put it back in park. Then check the fluid level) If it's low, add fluid to bring it to the proper level. DO NOT OVERFILL! If your problems persist, then the trans is going bad.
Unfortunately, if your transmission is failing, there's nothing you can do yourself but have it serviced/replaced.