Important !!!!!!!!!!----Unfinished Basement Insulation
While you work with insulation you should always wear long sleeves and pants and a breathing mask. I wouldn't worry about long term damage to yourself. Many people have worked with insulation and not worn a mask. Just wear one from now on.
If you are going to tear the paper (facing) off the insulation you can buy it unfaced already. You might even get a price cut.
Did you seal all the holes down there before putting insulation in. Don't seal around anything that gets hot, but exterior faucets, cables, gas lines can all be sealed with an exterior caulking and if you need to fill more use some expanding foam. This should seal it real nice.