The sensor itself isn't the cause of the problem, certainly. If it is reporting low coolant when you assert the level is full, the short answer is that it is contaminated and must be replaced. If a contaminated sensor is found it follows that the same contamination is elsewhere in the system, possibly the radiator. If the radiator is blocked, with these contaminants, the car will run hot. If contamination is the cause of both conditions then the flush did not accomplish what it was advertising, though a complete flush done properly would have a positive effect on any system that is not seriously blocked.
Confirm that the coolant fan comes on at the correct temperature, cycles itself off after a couple of minutes, and stays off for at least two minutes. A cooling fan that remains on without cycling indicates poor heat transfer in the system, meaning a defective pump, thermostat, blocked radiator, airflow issue or contamination.
Air bubbles from a leaking head gasket can trip a low coolant sensor and also be the cause of running hot, and can happen on the same day. Suggesting that this is the problem without first performing a cooling system performance test (described above) and pressure check is guesswork, but I do recommend a pressure test to eliminate bubbles as a cause. Note that a pressure test simulates (and assumes) the vent pressure cap is also working properly. A 70/30 mix of coolant boils at 230 degrees if not pressurized, and so the pressure cap assembly should also be tested to its rated maximum.