Yep, definitely want to be using gloves

Just out of curiosity, what colour electrodes are you using? I've found the gold-top or blue-top to be best for Al, and red (the radioactive ones) ideal for steel.
I also frequently dip the tungsten in the weld pool, or on the rod, and my reaction is pretty similar to yours. I've got quite good at "rejuvenating" the tungsten with a small hammer, without removing it from the torch...