1. You should have been honest about your fear of flying right off the bat and the rest of this story would have been avoided.
2. You should have owned up to leaving the safe open immediately.
3. You shouldn't have called the District Manager to whine about some degree of punishment. It doesn't matter how much money was in the safe, it matters that it will never happen again.
I'd tell you to take SamurAchzar's advice, but that would be a waste. You'll probably continue to let that playground mentality rule your office relationships and go bitching about your self-created problems to a union rep or corporate. After escalating the conflict even more, you will be targeted for firing after your next screw-up; however small it may be.