My furnace keeps blowing cold air and will not heat up the house. I changed the filter and it ignites and flames go on but do not stay on long before they shut off.

Check and see if your furnace has a flame sensor. It may be corroded or failed.

Yes it is the flame sensor/milivolt generator or your fan motor is not kicking on in time before the limit switch says fk it cut the gas off. In that case you need a fan motor of a cooler cut in time on your cam stat/fan limit switch. You can always turn the fan to on at the stat to isolate the problem. If it don't come on it is the fan motor.