You poor thing. Try not to worry about 'flashbacks'-you're processing the trauma of the event.
Your natural childbirths were expected, so were not traumatic in the same way as this, more shocking, event.
If you are really troubled, and feel that you are still in shock, or still feeling the trauma, then you may need some help to process it. I can reccomend a process called EMDR which is fast and efficient. You can find a therapist here. One or two sessions would be enough to help you to get over this.
Finally, you are not being a wuss. You have suffered a very traumatic injury-to lose the tips of your fingers means that you have effectively lost the use of one of your senses, touch, and it will also have left you incapable of doing many ordinary things we all take for granted. Go easy on yourself and allow your mind, as well as your body, chance to heal.
By the way, my Dad did this with a lawnmower, and his fingers were just fine once they'd healed, so the prognosis should be good.