It sounds like a bad fan/temp switch. There is a small box with a probe containing a bi-metal thermostat that turns the fan on when the temperature of the champer has reached a preset temperature. Often, these also act as a high limit. Their proper operation is crucial to a safe furnace.

well, it depends on how old the unit is, older will have a metal box about 8 in. above the burners, if you remove the cover you will see a silver dial, if it moves when the burners are lit, the blower should come on when it hits a set prong. replacing these should be done by a pro, as there are 2 different ways to wire them up.
Newer units use a snap disc which is a little brown plate about 4 inches above the burners with 2 wires to it, if the burners lit and no fan within 30 or so seconds, it is bad( flame will shut off due to high temp.) Shut the power off, remove the 2 mounting screws and take the part to a supply house to match.
good luck

outside unit keeps running when inside blower stops working. Is it something I should call a professional?. my A/C has been running just fine. I had the A/C annual service a couple of month ago and there was no problem.