What leaked out of small copper line when I blew a hole in on my air handler
If by "air handler" you mean heater/air conditioner/cooler unit, then yes you have punctured your refrigerant line. The big and small pipes are the in and out circuits, the gas will only be cold if it is on the appropriate side of the cycle and if the compressor is running.

This will be an expensive mistake. Your soldering job needs to be gastight, structural (won't pop off under pressure) and not introduce contaminants (like flux) into the system. Next time, disconnect the power.

If the unit is older (say > 10 years) you should consider replacement. If you are going to spend $700 on service it is well worth checking the cost of new units. If it is over 20 years old I would simply replace the thing.