Is it safe to be in insulated attic
Generally, it's safe to be in an attic with fiberglass insulation without a mask. Is it a good idea? No. It can get into your lungs and cause the coughing you're experiencing and can also irritate your throat. the coughing you're experiencing is probably a combination of the fiberglass and the dust that settles from the venting of the attic. Do yourself a favor and wear a mask.

@Chris Rodgers mentions about how much stuff adheres to a mask after just a short while and that reminded me of a photo I took last year after being in my attic for about an hour installing a whole house fan.