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It definitely sounds like the heater core has developed a leak. To confirm this, you need to have a cooling system pressure test done.
Here are directions to replace the heater core:
This is a Paysite
Getting coolant thru the vents is a sure sign of faulty heater core. An aftermarket heater core runs between $250-325, labor will run about the same. Figure $500-650 parts and labor.
As far as continued driving, whenever there is a coolant leak, even with you checking it every day, there is ALWAYS the possibility of overheating and causing further damage such as water pump failure, blown headgasket, or radiator failure. In addition, the coolant will start leaking onto your carpet at some point and staining it.