You may have it if it becomes chronic side effects see a doctor soon
I think that this is traumatic. And a traumatic event can trigger ptsd. For something to be a disorder though, it has to regularly impact your life. If enough time has passed and you are having symptoms, not sleeping, etc. then it is time to ask your doctor about it. And regardless of a diagnosis of PTSD, a counselor or therapist or psychologist is a great asset and resource for recovering from something that has been really painful as this clearly would be.
I'm very very sorry. Seeing your pet shot is like seeing a family member or loved one killed. That's how many feel about their pets (I do) so this would be emotionally devastating.
Are you feeling any better now with some time passed?