Hi and welcome to the LOC.
Your symptoms seem to suggest the problem is temperature related.
If the car seems OK when cold but not when warm it would point to the coolant temperature sensor.
When cold the fuel mixture is richened (used to be the choke on older cars) as the engine warms up the mixture is weakened to normal fueling levels. If the engine ECU, because of a faulty coolant sensor,thinks the engine hasn't warmed up it will continue over fueling and giving the problems you have.
You can check the sensor with a multimeter,either the voltage output hot and cold or it's resistance hot and cold, for what they cost just replace it but also check the wiring connections to it as well.