Deer in headlights?

So, in every science book I've ever read, movie I've seen...there is always mention of the human response to fear being either fight or flight. What happens if you fit into neither category but rather deer in headlights?
Perhaps it's that the instances in which I think I am really fearful subconcisouly I know I am fine so my reaction kind of sucks.
Examples:
1) A few years ago when I lived with roommates they decided to throw a midnight surprise party(super sweet and fun!) for me in my bedroom (after I had gone to sleep). A super fun idea, but they had concerns that I might attack them instead of celebrating simply because they terrified me. Instead what did I do? I screamed and swore. The girls, of course, laughed. And then we celebrated. But the point was that I didn't fight or flee. I sat straight up and yelled. Yeah, not so helpful in the case of an emergency.
2) This morning. at 5:45am the fire alarm was going off (and damn is it loud!). My reaction was to sit straight up and scream. Then turn on the light and look for smoke. I smelled it, but didn't see it. I turned on every light in the house. And felt then opened every shut door (not that there were many). The alarms went off. I promptly turned off the heat and the smell went away. I have since figured out that it was that gross burnt dust smell that happens when your heat really kicks in for the first time in ages.

But really? Who seriously reacts in that way? Where is the fight ot flight?
Yikes.