It depends on what it is. I've shrieked when startled, but I think this is in part my PTSD, because I also go into hypervigalence/self-defense mode. When I was 15, I dropped a wine glass on my food, causing a 3" long by 2" wide (guesstimating from memory) gash. I looked down, went, "Well fuck," and then went to the bathroom to start doing first aid. My sister nearly passed out when she saw the blood, when I asked her to call my parents' cell phone, she started wavering, I sighed and said, "Give me the phone," called my parents and explained the situation while cleaning the wound. I then had argue with Mom, who is a nurse, that "well, butterfly closures should handle it." I said, "No. We are going to urgent care. I am getting stitches. This is not up for debate." (I was an easy-going teen, so if I said something like that? There were reasons.)

I've had sharp intakes of breath but those have usually been shock at reading or hearing something really fucking horrible. For the most part, my reaction is not to scream. Granted, after the DSHS psych eval for disability cash assistance, which was stressy and in-depth enough to be actively massively triggering, I went out to the car, told my fiance to cover his ears, and just started screaming. It was not pleasant.

But horror movie type screams? No, I'm pretty sure my reaction to finding a dead body would be, "Well, shit, that's different." Really, being startled is the thing that tends to get a reactive shriek from me, but that's... really the only situation I can think of that being the case for.