Alrighty, first set of corrections is from the one with the young girl's point of view. Since it starts off in the present, as if she is currently at the school, any changes will be shifted into the appropriate tenses.
In the second sentence, there should be a comma after "1960" so that it makes a phrase. ("this Monday, November 14, 1960, I am")
The third sentence should be restructured slightly and split into two sentences. Also, "policemen" doesn't need to be capitalized.
"Four policemen will escort me, which my mom told me was for my safety. Some people don't want me in this school because I am black."
The fourth sentence looks fine except for the tenses don't quite fit. I'd suggest changing "feel" to "felt," as if this is from after she is away from her mother. ("I felt my mother's anxiety, and that scared me.")
In the fifth sentence, you can drop "they" before the word "terrorized." ("and insulting me terrorized me") Also, you can put the fifth and sixth sentences together, if you'd like. ("and insulting me terrorized me, because I don't understand what I'm doing wrong.")
The seventh sentence should probably be split up, as it doesn't really make sense right now.
"I'm just a little girl from New Orleans who was born with black skin. I am anxious about discovering this school, and all these people who want to prevent me from entering."
The eighth sentence, again just needs a bit of restructuring; correct phrases and whatnot.
"Despite the crowd being agitated and threatening me, and the fear that knots my stomach, I'm still happy."
In the ninth sentence, "white" should be changed to either "whites" or "white people".
Onto the second set, which is from the mother's point of view.
The first sentence the question "What time Mom?" makes no sense in this narrative, so I'd suggest just getting rid of it.
The second sentence just has a few small errors. There shouldn't be a comma between "daughter" and "is" ("my little daughter is one"), and you should put "into" after "integrate" because it flows better that way, and makes a bit more sense. ("to integrate into public elementary school.")
The third sentence seems perfectly fine to me.
In the fourth sentence, you can drop "that" and make sure all the tenses are the same.
"This hostile crowd insults us, and has launched tomatoes at us to deter us from entering."
In the fifth sentence, it all looks good, but I'd suggest adding "her" or "the" in front of "police escort" to show whose escort it is. ("despite her police escort" or "despite the police escort")
The sixth sentence should have "to" before "congratulate" ("to reassure her, to congratulate her").
The seventh sentence is fine.
In the eighth sentence, to make the tenses cooperate, I'd suggest changing "when she will be safe" to "when she is safe".
Last, but not least, the tomato's point of view.
The first sentence should probably be split up, and kept in first person.
"I was a beautiful ripe red tomato, ready to be enjoyed. I asked nothing of anyone, but suddenly found myself in the hands of an angry stranger."
Since the first sentence started in the past tense, and hasn't quite caught up to the present yet, the second sentence should be in the past tense as well.
"This man was full of hatred toward an innocent little girl trying to enter her school."
The third sentence needs a little restructuring in order to make more sense.
"I felt myself thrown through the air, toward the girl."
The fourth simply needs restructuring, as well.
"She certainly would've gotten hurt if I had hit her."
In the fifth sentence, I would suggest changing how you describe why the man missed.
"Fortunately, the man had terrible aim, and I crashed against the wall."
The sixth sentence doesn't make a whole lot of sense to me, but if I were you, I'd change around the sixth sentence, and put it together with the seventh sentence.
"I'm in agony over the fact that I was meant as an insult to this little girl, as I attend helplessly to the hate overflowing from this hostile crowd."
I hope this helps, dear. :)