You need the permission of the compiler for things to be accepted, and the compiler is denying you that permission. "May I do this?" "You may not."
May is just as strong as must. It's only weak in the positive sense, where once you're granted permission, you're not obligated to do it.
Fallen implies you are still in that condition. "I have fallen over" means you're lying on the ground and need to get up.
Fell is past tense and indicates something that happened previously, regardless of your current condition.
So, say you're at a party and have had a bit too much to drink. You fall over. You're lying on the ground wondering why everyone is sideways. "Oh," you realize, "I've fallen over." That explains your current situation. Before you figure out you need to get up, your mate comes by and asks why you're on the ground like that. Referring to what happened in the past, you tell him, "I fell over." He helps you up and you realize you're bleeding because you fell on top of and broke a glass table. When the ambulance shows up, you explain that "I fell over," even though, now, you're standing (more or less) upright.
Note that there are other contexts where this changes: Some years later, your friend asks you (because he was too drunk to remember that party), "Have you ever fallen over?" and you might reply "Yes, I have fallen over. Remember that party?"
Edit: In response to a comment... present perfect refers to the present or recent past (or a time frame that stretches to the recent past):
We tend to use the Present Perfect when reporting or announcing an
event of the recent past:
The company's current CEO has lied repeatedly to her employees.
But we tend to use the Simple Past when reporting or announcing events
of the finished, more distant past:
Washington encouraged his troops.
Source
See the referenced page for a simple explanation and more examples.
Best Answer
As has been already stated, they are both contractions of "I have not," and neither is incorrect. In the USA, I would say that "I haven't" is far more commonly heard. The use of "I've not" sounds a bit more proper and old-fashioned.