Our car smells like Band-Aids

It definitely is unhealthy to breathe aerosolized coolant.
Many years ago, I was unwittingly driving for several weeks with a leaking heater core, and the result was some very nasty lung problems.

You need to refill the coolant and carefully monitor the level daily in order to see if the level drops. If it does, I suggest that you get the car to a trusted mechanic a.s.a.p.

If it needs a new heater core, be prepared to pay…perhaps as much as $700-800 for replacement. The part is relatively cheap, but the labor involved can be incredible. On many cars, it is necessary to remove the entire dashboard in order to access the heater core, and I would be very surprised if dashboard removal was not necessary on your vehicle.