Welcome to Terry's Forums jp102,
What is the Model of your Carrier A/C unit.
You may want to try to put your Thermostat / Controller in Fan Continuous Run mode when it gets in that screwed up mode to further diagnose your problem, and see if you can manually control the blower.
As far as the compressor and blower starting at the same time, That should not be a problem.
Good Luck on your project.